Games with balanced, difficult challenges that you can't grind to beat. A lack of open spaces and waiting. I've rarely played an FPS with the balance of Quake 1 (where running out of ammo on harder levels is a valid concern), or an RPG with the balance of FF4 (You get these five guys today, deal with it). Coming up with your own solution is only fun if that solution is still challenging, and doesn't take grinding to get to. FF5, I'm looking at you.
Looting random scrap to sell for cash is terrible. A strength score that determines your carrying capacity is terrible, because you're trading a game advantage (other stats) for a personal advantage (not being annoyed by constant trips). Seriously, who maxes out their carrying capacity with /useful/ objects, short of Nethack?
Weapon balance that isn't awful. I'm looking at you, almost every game.
Sniper rifles in an FPS should only occur in a sniping game, unless it's multiplayer. Sniping games are very different from other games. Sniping in Fallout:NV, or Borderlands, or anything else: "I'm going to sit here on this rock and shoot you and you can't run up to me in time to kill me, sucks to be you, boy this is boring". Run-and-gun shouldn't really occur in a sniping game, because it sucks: "God damn it, why do I have to dodge these mortars, this isn't the game I paid money to play." The only games I've ever seen pull off a multi-game-type combination in a way I enjoyed was, uh...Modern Warfare, because it was practically a minigame there. Of course, then they blew it by turning it into an escort mission, with a guy who couldn't move.
No escort missions. Defending someone else sucks.
No "hurry up and wait". I'm looking at you, Hitman series.
Dialogue options should either be selectable by number (every good RPG) or proceed automatically when selected by a button (Alpha Protocol). AP was awesome. Instead of "wait for the other guy to say something, then conversation pauses while you pick something", it was "pick your stance, change it whenever, conversation isn't going to pause for you". Kind of like Mass Effect 1 but with no pauses. It was great.
Equal rewards for being a good guy and being a dick. Alpha Protocol did this very well, and aided roleplaying. You got a bonus if your handler likes you. You got a different bonus if your handler hates you. You get a perk from letting an arms smuggler go, a different perk from arresting him, and a different one still from shooting him in the head.
Multiplayer co-op games should have assloads of variance. Left 4 Dead did this to a godly extent. You can play a mission four times and hear four different banterings between your teammates.
If two NPCs are voiced by different people, never give them the same lines. Ever. Taking an arrow to the knee is just the most obvious example, but a good 3/4ths of games with random townies walking around do this.