A few sessions would normally be enough for me, but like others have said it also depends on the type of game. I find that, for me, the RTS and Action adventure (usually third-person) games will necessitate more play time to see most (if not all) features of the game. Sometimes you have a game's starting point or "tutorial" which can be boring and gives a false impression for the first hour or so when finally you realize after a specific point that you were actually just going through some tutorial and you're "now" finally playing "the real thing" and it gets better from there. One example I can think of is TES Oblivion, sure I liked the graphics the first time I popped in the prison cell and played with the hanging chains to check the physics but then it was tedious to walk and escort the trio and the king until you finally get outside to the breathtaking scenery.
I would say that Fallout 3's tutorial was better than Oblivion's, but still boring to get through and couldn't wait to get outside, but at least I knew then that it was just a repeated game-play mechanic and that I was actually just going through a tutorial (which I wasn't that well aware of when I played Oblivion, considering that Morrowind's "tutorial" on the boat was probably just five minutes long so I never really considered it as such in Morrowind, to me Bethesda really started with that whole tutorial stuff with Oblivion, at least in length). As for an actual 3D action adventure type of game it's been many years but I'd have to say Shadow Man. The first hour or so felt awkward, thought I didn't like the game's story or setting much, but kept playing and suffice it to say that to this day it is still installed and it ended up being one of my all time favorites (and I wouldn't have known about it had I just stopped playing when I felt it was boring during the first hour or so back when I first tried it on the N64, but later ended up buying it on the Dreamcast).
With RTS games (depends which ones) I usually wait until I've seen much units, or tech upgrades, or at least a good portion of the game's campaign(s) if available. There's one exception though, Empire Earth III which I've mentioned recently in another thread. That one... well I think I've played it for maybe three hours or something like that, can't remember but it wasn't much time and ended up uninstalling it, but that's an exception to "the rule" (for me). Another example I can give is Dawn of War 2. It took me lots of patience going through the campaigns (with expansion pack's campaigns) since I never really liked the game-play style overall and I actually enjoy The Last Stand game mode almost exclusively (when on the other hand I really liked DoW1's campaign and regularly play skirmishes with that one). It still took me maybe two days playing DoW2's campaign until I "realized" that I was actually bored with the game (but kept going to follow the story and didn't want to just watch the CGIs on YouTube).
So yeah, it varies from game types to game's stories (if the story is good and the game-play is bad, chances are I'll keep playing anyway) or game's features (when I want to see all features before turning the switch off when I'm bored with it). The type of games for which I find it "easy" (fast) to know if it's bad or boring are purely action-oriented FPS'es, fighting, racing (car controls immediately tell me if I'll like it or not right from the very first track regardless of anything else), puzzle or purely story-oriented games (with story-oriented games I need to get immersed right away, otherwise the rest won't matter to me and I'll uninstall).