When I first joined my Thursday Night campaign, I rolled up Staab the warforged ranger—a straightforward, polite, cooperative member of his new party. After all, as a new player, it made sense to fly under the radar.
Staab bored me to tears.
By the time we started playtesting 4th Edition, it was the perfect time to roll up Garret Farwhere, halfling warlock. Garret's personality better matched my preferred gaming style: the instigator.
In my mind, instigator is a nuanced role. It combines elements of a trickster, jester, intrepid explorer, and—at times—damsel in distress. Essentially, you're trying to maximize your own fun at the table without diminishing the fun of the other players. However, you have to walk a fine line between keeping things interesting for yourself without annoying, antagonizing, or outright jeopardizing the rest of the party. The guy who opens random doors in the middle of a fight just to see what's behind them, inevitably drawing more monsters into combat, is all three of these things. That type of behavior doesn’t qualify you as an instigator—in my book, that makes you a jerk (or a Cylon).
That said, an instigator who takes the occasional random approach to a fight can sometimes elicit better results than the rest of the party might expect (think of Wicket luring off those Stormtroopers outside the shield generator). In his most famous success to date, Garret, along with his bold companions, fought within a treasure vault, the treasures stored behind a series of force fields. As the rest of the party battled the guards, Garret teleported behind the fields to see what he could take (thinking to help out the party, of course). Knowing the type of character Garret was, the DM had prepared a surprise: a "sleeping" chain golem within one of the vaults, complete with an alluring lock on its waist just waiting to be picked. Garret managed to pick the lock, but activated the golem at the same time. Without the command words, he had to teleport out of there in a hurry. But near the end of the fight, he used another power (will of the Feywild) to teleport the final enemy into the force field—and beneath the smashing fists of the golem.
Other times, marching to your own beat occasionally does mean pursuing goals that may or may not correspond with your party's. Take the Eye of Vecna for example. In our campaign, we were running through Thunderspire Labyrinth, and the Eye made an appearance. The rest of Garret's party wanted to destroy it … but Garret desperately wanted keep for himself. He even tried to pick a fellow PC's pocket to get at it. (He made the attempt, in a stroke of metagaming genius, by using an action point to make the Thievery attempt mid-combat so as to not look inactive for a round.)
Garret never did get that eye (nor, for that matter, did he get his mitts on Moran’s Eye from King of the Trollhaunt Warrens). But really, that was never the point. The point is that as the instigator, Garret helped move things along, without completely moving counter to the goals of his fellow party members. It's a challenging role in a cooperative group dynamic, but if it fits your style as well, I'd fully encourage you to not take the most strategic action every round, but think about exploring the most interesting one. I firmly believe that most DMs love it when you do. In the end, their monsters are meant to be defeated and their villains' plots unraveled. If you can help do so in a way the whole table remembers—that makes the adventure all the richer.