If you're looking for, "Realistic" Modern Military shooters, then first and foremost, I suggest Call of Duty. CoD gets hate mainly because its formula gets copied to death, not so much because its formula is BAD. It's a very intuitive, streamlined series of set pieces designed to invoke exactly the kind of aesthetic these kinds of games are going for, and if you don't go into it with you Games-Are-Art Beret on (A piece of headgear I myself don nearly constantly, mind you), then you can have a pretty damn good time blowing up all the guys. The first Modern Warfare probably holds up the best.
If you want multiplayer, it's hard to beat the pedigree of the Battlefield games. They might be the most enjoyable multiplayer of the bunch. Bad Company 2 is great if you don't want things overly serious, the latest Battlefield game if you're fine with more, "Realism".
If you're looking for something that feels a little bit more tactical, I suggest the Rainbow 6: Vegas games. They probably pioneered the cover based shooter in some respects, and probably make the tactic of hiding behind cover feel more meaningful and tactical than any other cover system I can remember. Plus, they arn't a COD clone, so it immediately feels more fresh. 2 is better than 1: If I remember correctly, you can't run in 1, which is a paaain.
How about playing as SWAT? The SWAT games are a blast, especially co-op, mainly because you have to deal with non-lethal weapons and hostages. It feels just a bit like a sim, and are probably the most different of the bunch.
And lastly, I have to mention Spec Ops: The Line. This is actually almost unfair, since Spec Ops is really a vicious deconstruction of the modern military shooter, but technically, it is a modern military shooter. It's story heavy and a SERIOUS mind screw. So really, it might not fit your criteria at all. But it is a MMS, and it is top notch.