Unreal series.
Unreal series is classic old-school shooter. Must play stuff, if you are tired or need a break from modern-style shooters. I don't really think U1 or U2 are that much of an arena shooter in the single-player campaign modes as they're more classics in style (especially U1), unless doing the MP portions. Unreal Tournament and the MP-focused stuff certainly are arena-style - and back in the day, were an absolute blast.
STALKER series.
Without any mods: tough as nails, even on easy. Absolute blast of a game. Absolutely memorable; atmospheric as can be; creepy as hell & scary (and I often don't scared at these kind of games); and one of those early FPS's that I think pioneered & championed the open-world experience for a FPS. Though, Boiling Point: Road To Hell (AKA Xenus 1 - starring Arnold Vosloo of Mummy series fame; and man do I love that game's theme) was probably first and had more RPG elements in there (as you have stats and stuff of that sort). Regardless, STALKER series is great and certainly felt like it was fresh and one of a kind when it came out. A must-play series, for open-world FPS fans and fans that want something that's tough as nails.
For me - STALKER: SOC and Call of Pripyat are the best ones in the series. SOC (Shadow of Chernobyl) felt fresh as can be and so new when it came out; Call of Pripyat felt like a much more polished experience than any of the others. Sure, Clear Sky is good b/c it's more STALKER: SOC - but it felt like it rehashed, remixed, and whatnot lots of maps, areas, and assets from SOC; and some of the new ideas here (i.e. Faction Wars) and the engine felt half-baked and/or unpolished. Still, don't write Clear Sky off - it feels more like an expansion than anything; and it's still good being that it's more STALKER.
Far Cry series.
Where to begin? A very consistent series.
Starting w/ Far Cry 1 from Crytek, absolutely revolutionary game engine and FPS at that time - feels like the precursor to the eventual open-world FPS's that came afterwards. With huge open-spaced maps & not-entirely always linear levels to battle in and go through; and looked great when it came out. Story was nothing special, but the game was.
With Crytek gone (off to go do Crysis with EA), Ubi made Far Cry 2, which followed in the footsteps of other open-world FPS's like STALKER series and Xenus/Boiling Point series - which was good, but didn't feel like it was entirely there yet. Too many cut & paste side-quests, which was also a problem especially in AC1 - i.e. the common Ubi problem. It was disappointing to me, but still good...and having the potential to become great.
Enter Far Cry 3. To me, still the best one in the series; and the formula that most FC games follow. Open-world FPS; lots of variety in side-quests; and an amazing villain. Michael Mando (Nacho from Better Call Saul) is amazing and iconic in this role, as the crazed pirate. To me, this was FC series at its best. Sure, FC4 is really good; has a great villain in Pagan Min (played by Troy Baker); and is probably more polished than FC3 - but it's more FC3 but in Kyrat (i.e. their version of India). It just didn't have the magic that FC3 did and the fresh-ness FC3 has. Yes, FC5 is really good also and also has a cool villain (Joseph Seed, played by Gregory Michael Bryk).
Dying Light.
Did you like Dead Island? Dying Light is that, but better. Dead Island was basically an open-world first-person action/ARPG; it was mostly focused on melee. Basically, this is Dead Island and much more improved w/ polish and new features. With day & night cycles; better feeling combat; polish; and parkour elements - it feels like a more urban Dead Island. And it's awesome.
And, I need to finish it, at some point.