Bolt-action, lever-action and other semi-auto, preferably old-school repeater rifles. They have a nicer over-all feel to them, and they're the only ones I find consistently works in games like they work in real life. Which obviously means they're ridiculously underpowered compared to everything else. But they have that nice "thump" to them when fired, so that you can almost feel how the recoil hits your shoulder.
Also, "real" assault rifles* are a favourite of mine, when portrayed right. That is, not an SMG with lower fire-rate and longer range. Preferably they should have select fire, or at least burst/semi-auto instead of always being full-auto weapons that basically work like a LMG.
Note that this is my opinion of guns in games, not a "fact", thus you can disagree with me if you want to. Also, the games you think of may be games I've never played, so there's no need to point out to me that I'm wrong about "X game" or stuff like that. /flameshield
*a lot of weapons in games are called assault rifles even though they're often actually assault carbines. There's a pronounced difference between a rifle and a carbine, the carbine is essentially the middle point between a rifle and an SMG.