For an excellent old school shooter with a need for some serious skill to get through the harder stages, Serious Sam 3 would be right up your ally.
For something with a bit more ambiance, Bioshock and Metro 2033 are excellent, excellent games. Metro in particular being a very well done survival "horror" game, while Bioshock delivers a story that's now pretty much considered a classic.
Dead Island delivers first-person melee combat really well, which a lengthy campaign and some firearms that are much better balanced when you install a mod or two to make headshots an instant kill and ammo purchasable.
Both Deus Ex and Deus Ex: Human Revolution are some of the best first-person RPGs available, with the first Deus Ex being more RPG than shooter, while its sequel is much more-action oriented than the original.
Borderlands mixes the Diablo style loot system with some competent shooting mechanics, so it ends up being pretty addictive. Though the sequel appears to have much more variety in terms of landscapes and interesting characters compared to the first, so if you've money to spend, that might be the one to get.
And finally, Black Mesa is a completely free mod in which all you need is the free Source Engine off Steam, and it recreates the entirety (minus the Xen levels, but apparently its in the works) of the orignal Half-Life, and even goes so far as to mix up some of the levels around in their layout to make it feel both nostalgic and fresh at the same time. It's really an impressive mod, and a better "HD Remake" than most the stuff big-name companies put out.