I never used to, but after Steam added the feature I started to. The screenshot manager makes it easy enough to delete the bad ones, it organizes all of the folders for you, gives you a place to share them and view other friends', etc, so it can be kind of fun to do and takes almost no effort. I do take a lot more screenshots than I ever post, though, and often times it's just to change the background image for a game in Steam. The only non-PC based game I've ever done it for is Forza.
I used to, but I got sick of posting 'em online for strangers, and they don't look as good as actual wallpaper for background pictures, so I stopped doing it.
I mean, sure I get 10 or 10000 amazing screenshots of an amazing game I played, and then what? They take up space is what they do.
By the time I'm done playing an average length game (Let's say 12 hours or so) I fall somewhere around 300-500 screenshots, much longer games, the sky is the limit, I have 1000+ on stuff like Borderlands, and I don't even really like Borderlands, Mount and Blade Warband probably has 1500+ or so, I will once and a while go through them and delete stupid ones, but I just like having them, silly things, pretty things, wallpaper worthy things, showing them to my friend things, I just love doing it.
Stupid EA, Origin doesn't do screenshots, how can the world continue without me taking a shot of Commander Shepards ragdoll going all crazy? It can't, it can't continue, again, ever.