I run both an in-person game and an online game. Both had two players (until an online player decided that he no longer had need of creative pursuits in his life).
The online game is played on the Psionics IRC server using mIRC. We would all open two instances of mIRC, with one as CharacterName or GM (in my case), and the other as our first name. All out of character questions, comments, and jokes were done using the OOC login, and only in-character actions and words were handled through the IC login.
I use a lot of music in my gaming, with each person, place, thing, and event having its own theme. I'm still able to do this using mIRC thanks to the Sounds folder. Before each session I'd send the players a zip file containing the music for that session, and they'd add it to their folder so I could have it play during the session with an IRC command.
One of my players made us a pretty simple dice roller using mIRC scripting. I think he set it up himself, but I'm not sure. Either way, a quick type of /droll 1d20 or /dradd 10d6 gives us fast and furious dice rolls.
The strengths of online gaming for me are as follows:
1) The Man Behind The Curtain.
On more than one occasion since doing online gaming I've ad-libbed an NPC or escalation of a fight or interaction that the players are having. I can page through notes, look up names in my mythology book, or use Google Desktop to find the name of the professor they spoke with 27 sessions ago. While I would call myself a pretty damn good GM, I don't have a great poker face or a perfect memory. This helps me out a lot by not distracting them.
2) He Said/She Said
The King of Homeland is about to send our heroes off to the Land of Early Dismemberment, but the Captain of the Guard feels this is a bad idea, and he and the king discuss this with the players chiming in. It can make for great drama, but also confuse the players with just which NPC is speaking at that moment. Using IRC to game, I just have one login change to "King" and the other to "Guard Captain" and the problem is solved. I find it makes NPC/NPC conversations much easier.
3) Bucket O' Dice
Rolling 15d8 is really fun, but adding it up the sixth time you use that spell is not. Using that script, /dradd 15d8, drops the total on the final line. That saves between 15-120 seconds per turn, depending who's going and how much they're doing. Not everyone is great at fast math, and I have players that are like that.
4) Scheduling
One player works full-time and goes to school full-time, and is battling car trouble. The other player, before leaving the game, attended law school over a thousand miles away. This pretty much was the only way to game.
5) "Marsha!" "John!" "...Marsha, you've got a pretty manly voice there."
A recent session had one player, a swordsman cursed with immortality and a dark past he only recently came to remember and understand, travel to the final resting place of his long-dead lover, a female summoner that he killed a thousand years earlier. The session was a pretty intense and emotional one, with her snapping at him that she thought he -loved- her, but he'd only been using her the entire time and killed her when he had no further use for her. He protested that he'd changed since then, that he understood what happened before, but he knew that was no excuse. This continued for some time, and after the session he told me that he was able to forget it was a 24-year-old guy typing that to him, and that had the session been done in person it would have been considerably less impactful.
I really enjoy online gaming. I think I may try my hand at finding a game after I finish running my current one, and seeing what life is like as a player. It helps that my car sucks and I can't drive further than about 5 miles at a time right now.