I'd agree with Quake Live, certainly fits the bill as a generic FPS since it is:
-Primarily deathmatch focused
-Traditional FPS design, i.e. respawns, items to collect etc rather than worrying about special gametypes, classes, buying weapons, unlocks etc etc
-"solid" physics model that is neither realistic nor as extreme as the likes of Quakeworld
-Reasonably n00b friendly in the sense that it has training modes, runs in a browser, doesn't need high end hardware
-Isn't as heavily focused on item management as some, you can be effective with more than just a couple of weapons
A key point to note is that "generic" doesn't necessarily mean "easy" or "popular".
-Primarily deathmatch focused
-Traditional FPS design, i.e. respawns, items to collect etc rather than worrying about special gametypes, classes, buying weapons, unlocks etc etc
-"solid" physics model that is neither realistic nor as extreme as the likes of Quakeworld
-Reasonably n00b friendly in the sense that it has training modes, runs in a browser, doesn't need high end hardware
-Isn't as heavily focused on item management as some, you can be effective with more than just a couple of weapons
A key point to note is that "generic" doesn't necessarily mean "easy" or "popular".