As a GM, I love non-linear thinking, but it tends to drive certain GMs/DMs up the wall.
In a Greyhawk game I played in very early 3E, I was playing a wizard with a mostly rogue and bard group that worked for the thieves' guild in the City of Greyhawk. The campaign was essentially our (mis)adventures working for the guild. On my very first mission, we were assigned to break into a dwarf's house in the Artisan Quarter and steal a deed for a mine in the Cairn Hills. Apparently, the dwarf was missing and someone wanted the deed before it got snatched up by the authorities, no questions asked. The DM started asking about who was casing the joint before we pulled off the caper, if we wanted to bribe the watch, how and when we wanted to break in and so forth.... Until I told the DM that I wanted to purchase an aristocrat's outfit and impersonate a noble from a distant land, with the pretense that this dwarf owed my noble master the mine as security for a loan he defaulted on. It's not like they could ask me to hold while someone called every noble's keep in the Gran March and checked out my story, right? We figured that we could just waltz in and take the deed and leave town with it and avoid a fight altogether, and whoever else was looking for the deed would go off on a merry chase to the other side of the Flanaess while we headed in the other direction with it. I even offered to back up the entire thing with a charm person spell and the hefty Bluff checks of my rogue and bard companions.
As the other players got in on the idea and started pitching in contributions to pull it off, the DM stared at me blankly. After a moment, he flat-out told us that the was genuinely impressed with our creativity, our plan was awesome, and far more clever than what he thought we would come up with, but we couldn't do it. Why? Because "there wouldn't be an adventure." We either do a breaking-and-entering thing like thieves are supposed to do and he planned for or there's no adventure that afternoon and we all go home. That was pretty frustrating, but at least he was honest.
Many years later I ran into a similar situation when I played in a Pathfinder Society scenario called Shades of Ice, Part I: Written in Blood. Since I don't get to play very often, I decided to go all-out and play my favorite character type: a clever illusionist. The setup is that the group has been sent to a northerly place called Trollheim in search of a guy named Rognvald Skagni--I don't really remember what we were supposed to do when we found him. Anyways, we get to his house and a gang of thugs ambush us. When my turn comes up, I ask the GM if the people here are afraid of trolls, he replies yes... So my illusionist promptly uses ghost sound to make the rumblings of a troll from within the house immediately after I yell, "Chomper, fresh meat!" On my next turn, I use silent image (my guy is still 1st level) to make an illusion of a troll emerge from the house, chewing on a humanoid leg and seeming very excited to see the thugs. The GM pauses for a second, then tells me that these guys don't believe that a 1st-level wizard could summon a troll. I ask how they can tell that I'm 1st level... He stops the game for a second, looks up the spell description, then hands me a marker and to draw in where the troll illusion goes since it's got an area of effect. I do, then he allows me a Bluff check to convince the thugs that it's a real troll and not just an illusion. I roll a 19 and have a +2 Charisma modifier for 21--he begrudgingly has some of the thugs shoot their ranged weapons at the illusory troll and then declares that the spell ends because the thugs interacted with it. Although I knew that interacting with the illusion allowed another save instead of automatically ending it, I bit my tongue and dropped it.
We ended up capturing some of the thugs and questioning them. We find out that they were hired by a "Hjort" and "Runa", then I tell the GM that I'm studying the dead boss thug intently, with the intention of impersonating him later with disguise self. Once we find out that Hjort and Runa are staying at an Inn called the Horned Helm, we're off. I work out a plan with another character and we tell the GM about it--I want to use disguise self to impersonate the boss thug we killed at the house, get information from them, and offer to present the "captured" pathfinders for extra money. We want to set up an ambush for them since turnabout is fair play. As soon as we get to the Horned Helm, we find the Hjort decoy at the bar, who inexplicably yells out, "you're Pathfinders!" before we get a word out and provokes a bar fight. Me and the player that came up with this plan share a look across the table that speaks volumes... Then my wizard runs for cover and waits for the bar fight to play out.