Half life 2 series. Incredible characters (and one of the few games that made my sympathize with the villain without being the villain (ala Overlord) and several moments I wondered why I couldn't join the combine). Alright the shooting is ho-hum perhaps. Not bad, but theres little that can't be solved with shift+w+M2 with the shotgun. The immersion is incredible, and it's hard to not be drawn into the shoes of Gordon (plus valve's sense of humor persists as they mock his muteness). There are some truly epic moments, such as the prison in Half life 2, as well as the final battle (no spoilers for you) in episode 2.
Next is, without a doubt, TF2. It is one of the most balanced, non-grenade spammy, shooters know. It has no regenerative health, so you know exactly how close you are to death (see cod), has no grenades or insta-death rockets (see TFC or HL2 DM), is INCREDIBLY balanced all things considered, and has enough unique things to prevent it from feeling cookie cutter (Ubercharges, Rocket jumps (though i have seen these preformed in other games, these feel fluid and natural) Backstabs, fire, and lest we forget THROWING BOTTLES OF URINE).
Sorry for the wall of text