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SPEC OP is the exact opposite of what you're looking for. It's a biting satire of modern military shooters and uses the mechanics of those games as part of it's message. It might be interesting to pick up if you're interested in that message or you could just watch the Pennyarcade Extra Credits about it.
I usually class old school shooters as having a lack of iron sights, no cover system, no regenerating health, large maps, not being on rails, secrets and puzzles, lots of baddies to kill at a single time, no AI companions (or they stay out of your way), player being a one-man army, a large collection of weapons, fast movement speeds, usually highly skill based, no kill streaks, a general lack of seriousness, finally generally not being a massive gun-wank about the American military and slaying improvised foreigners.
Modern classic shooters that come to my mind are (in rough order of new release):
Painkiller
Primal Carnage (Asymmetrical multiplayer old school arena)
Tribes (multiplayer old school arena)
Serious Sam
Nexuiz (multiplayer old school arena)
Hard Reset
Resistance 3
Valve titles
S.T.A.L.K.E.R. gets an honourable mention not because it's a classic shooter (although it does have elements) but is an example of a "realistic" shooter done right.
I'm sure there's more but it's too fucking hot to think right now.