I am very fortunate to have several campaigns to run. (I can thank MapTool and Meetup for this.)
Here is our current campaign schedule and some info on the orientation of each game:
Story-Oriented
Age of Worms: We played this one from 1st to 20th last year, and it was a lot of fun. Characters had some interesting backstories, but our table's primary goal from the start was to create a lasting campaign. Prior to this, most of the campaigns I played in were very short and involved a high amount of turnover (they took place at a FLGS with strangers for the most part). A couple of us who 'regularly' attended these games (i.e. more than once) wanted to form a group who met away from the FLGS (which, btw, no longer exists). We made a pact to start a campaign and stick with it from 1st to 20th, and I was going to DM.
I was inspired by the Whispering Cairn and set out to run our first Adventure Path. We had played a few Eberron games at the FLGS, and some players (including myself) wanted to play warforged and shifters, and I knew I could wing the Eberron stuff easier than any other setting (except my own, but I didn't have the free time to build one). In 2005 our table of 8 began our journey.
Around the time when the party was 'supposed' to leave Diamond Lake, two (out of now seven) players wanted to abandon the Path. One of them took a look at the map and wanted to go anywhere other than where the main plot hook (Allustan, aka Gandolf) wanted them to go. He was testing the World orientation; he wanted to explore rather than follow the plotline. The rest of the table disagreed.
Another player was fascinated by the politics of Diamond Lake. I had integrated all of the character backstories into Diamond Lake (a warforged cleric was to cleanse the corrupt Church of the Silver Flame, which IMC turned out to be a leg of the Ebon Triad, an elf wizard was an attendant of the elf mine manager, a dwarf rogue was a mining expert who had a strong relationship with the dwarven clan, etc). One of the characters (the dwarf rogue), due to how he setup his backstory into the campaign, very much wanted to stay in Diamond Lake. At the time, one of the mine managers lost their mining rights (due to the result of the AP) and he very much wanted to work to get the dwarven clan to get rights to the mine. More importantly, it wasn't something he simply wanted to 'gloss over'; he wanted the campaign focus to shift to this aspect, with weeks of intrigue and for him hopefully some adventures to help the dwarves in their plight. None of this is in the AP, and most of the other players just wanted to follow the main plot hook (leave Diamond Lake), which is what the table voted on doing. Sure, I could have done a lot more work to make that player happy, but it would have been at the expense of prepping the next set of adventures (and it could have significantly changed the campaign).
Last year, after a year and a half of playing, we finished the campaign. Sometimes I wonder if the group would still be together if we didn't have a clear goal of "1st to 20th", thanks to the AP.
Shackled City: Another DM (a player from the original group) took the weekly Wednesday night slot when Age of Worms ended. He is running Shackled City pretty much like Age of Worms. We have very little character integration into the campaign, although having a base of operations in Cauldron is very helpful for character development. (My coistered cleric started making small humble celebration meals after every adventure but they are slowly turning into grand events, with all of our NPC friends attending). However, it doesn't seem like any of our backstories or personal playstyles are actually affecting the adventures; if you've played Shackled City and sit down at our game, you'll probably recognize pretty much every encounter. For World-Orientation, after playing AoW, our group has adopted the mindset of "follow the lead hooks", and so far (we're at 7th) none of us has ever said "Let's leave Cauldron and just explore". And even the story so far has been rather 'bleh'; it's very cinematic. Right now we're 7th level and going up the steps of a Koa-Toa compound. Does it really matter that we're looking for some dwarf or whatnot? No, because the action keeps us coming back every week.
War of the Burning Sky: This is one of our online games we started a few months ago, and we just finished the first adventure (we're at 3rd level). The players LOVE the story, more so than Age of Worms or Shackled City. In fact, it's so enjoyable that it inspires a great deal of roleplay with the NPCs. The action is awesome (one player, who rarely calls me outside of our games, had me on the phone for an hour discussing one of the battle scenes), but we find ourselves doing a ton of roleplay (many sessions with no combat at all) because of the story. I also added a little more character integration, and thanks to EN World I was even able to get a mount that he very much wanted for his character (a giant eagle) written into the Path!
However, the story is still the star of the show for this campaign. There was a near TPK (one player might escape) on Thursday, but thanks to MapTool's chat logs I miscalculated the damage done to one of the villains. I presented a few options to the players: make 2nd level characters to join the lone 3rd level character, wait to see if the 3rd level escapes (she probably won't) and start over as 1st level characters (meaning I would have to make new adventures related to the story), rewind and redo from a certain point, or start a brand new campaign. My players hate rewinding, but all of them wanted to in this case, not because they felt it was unfair, but because they love the storyline so much and want to reduce the risk of having to abandon it.
Action-Oriented
Savage Tide: This started out as our first weekend game. We had a few other games on the weekend, and one player could only play once a month on the weekend, so I decided to run Savage Tide as an abridged, marathon hack-fest. We are now 15th level, having wrapped up City of Broken Idols last night and beginning Serpents of Scuttlecover next month. There's still a decent story here, but it's primarily a series of battle sequences and leveling up exotic characters, and this can be very enjoyable if you want a chance to power game. Also, a few times I've run this as our local area Meetup game, and at one point I had 12 players (we were around 8th level at the time). Players showed up with their characters and had plenty of time to socialize, talking with others about their stats and builds while they waited for their initiative to show what they can do. In one session we did have a World exploration oriented game (Tides of Dread) where the Isle of Dread was placed in the center of the table and players decided as a group where to explore. Lot of random encounters, and we even split up the group with two DM's running the show.
Living Greyhawk: I'm sure others will have something to say on this, but I really see Living Greyhawk games as 'Action-Oriented' more than anything else. That doesn't necessarily mean they are always 'exciting', they just tend to involve a great deal of combat (and in LG's case, sometimes very difficult combat). And not just LG, but also the majority of Con games I've attended. When you're put in a room with strangers and have a limited amount of time to play, you have very few options. In Living Greyhawk, most of the modules are more linear than not (and in their defense, Dungeon and pubilshed modules are generally like this too). So while story and roleplay can be very important, there is usually zero character integration (you can't change the module, for the most part, to tailor it to a character's interests) and there is usually zero world exploration (some DM's have actually said "if you don't want to take this mission, you are welcome to leave" and then, IRL, actually point to the door and refer to the player). What does everyone else think?
Expedition to the Demonweb Pits: I'm about to start a new campaign online for Demonweb Pits. I was inspired by a game I played at ConQuest Sac: the Ultimate Cheese challenge (which I won). I wanted to have an opportunity for some of our players, who love character optimization, to build something nasty. Gestalt, 50 point buy, all WotC allowed, and Monster classes are treated just like base classes with no entry or exit restrictions. So I have one person with a chain devil monk, another with a deva cleric and another with a succubus dread necromancer. The catch is they are only 7th level, and we only have three players. No backstory, and while I haven't really read the plot I'm guessing I can piece together a lot of cool fight scenes from the book.
World-Oriented
Mysteries of the Moonsea: I started this game a few months ago online, and so far it's been a lot of fun. We started in Melvaunt, and players have roamed the city looking for adventures and getting in trouble with the various Houses. Right now one of them was captured by House Bruil, and using a new character as a hireling of the party the House has given them a few missions in exchange for release of the old character (who is the sister of another PC). House Bruil has also exhiled them from the city until they return from an expedition to Thar. Right now they are deciding if they want to sneak back into Melvaunt, go to Thar, Glister, Thentia, Phlan or a Pirate's Cove (one of the other players is a Pirate). There is a moderate amount of character integration, a ton of opportunities for world-exploration, no driving metaplot and some combat but nothing exotic (mainly against human fighters and NPC classes).
King of Sutter: This campaign is another monthly game I use to introduce new players to D&D. It takes place in a homebrew medieval version of Northern California. Players are encouraged to go where they want, but they usually opt for the 'newbie' quests of the nearby mines in the Sutter Buttes. These mines are big, custom made dungeons that give new players the chance to learn the mechanics of the game. So while it started off as a world-oriented game, and I have integrated the backstory, because there are always new people showing up it usually turns into dungeon crawling and combat exercises. (We have 29 members so far in our group, but only a core 10 who are in regular campaign, so we usually have one or two new players every game.)
Tale of Sutter: Also, taking place in the homebrew world mentioned above, this game takes place on the Wednesday nights that the Shackled City game is canceled (which happens somewhat frequently). Although there is opportunity for world exploration, because it's just a 'backup game', and because it's quite a deadly campaign (some refer to is as the 'Curse of Sutter') it tends to lean towards hack n' slash.
Character-Oriented
Trust in the Party: A few months ago a player wanted to me to run a new campaign online during a time when he could play. He wanted the world to have a solid base of operations, and he wanted it to involve a lot of intrigue and espionage (this player runs a Spycraft game on the weekends). I got a few players together and using their backstories I decided to make a game in Sharn about secrets and blackmail. We brainstormed for a few sessions, and the three players came up with different character: an artificer, a bard and a rogue. Each needed a deadly secret that only the other party members knew about. The bard served for the Brelish army in the Last War, but he was secretly using a stolen message stone to communicate troop movement to Karrnath. The rogue is a changeling, disguised as a House Sivis operations; the Tyrants are using him to extract secrets from the gnomes. The artificer is a thief; he developed a 'reduce construct' infusion and used it on a warforged scout to create the ultimate sneak.
Each backstory is tied to one another. The artificer's warforged stole information from the Tyrants, revealing the true identity of the changeling rogue. The rogue unlocked information from a message stone revealing the bard as a traitor. The bard, now working for the Korranburg Chronicle, tracked the story of the warforged scout and revealed the artificer as the puppet master behind the crime spree. Each is blackmailing the other, and now work together to blackmail the various organizations in the City of Towers.
We were set to begin this game last week, but then one of the players had a change in work schedule and can't participate in this campaign anymore (he players in others though). A third of the material I had designed for the campaign is now worthless.