So my wife and I had a baby a few months ago, and as much as I love gaming, I am finding it impossible to get more than a half hour block of time. It makes it tough to really get into games with lots of quests, dialogue since you pretty much forget what was going on and lose the "immersion". I think what I need is something like UT2004 (maybe I'll even get it again since I lost my play discs) which I used to just play against the bots for a quick reality escape. My dream game would be some kind of an arena where you might be able to add on equipment / abilities as you won duels that don't take too long. I never followed shooter games too much being more of a TBS guy so maybe I missed something - is there anything out there like that? thanks

Well, the only game I can think of that comes close is [url=http://en.wikipedia.org/wiki/Star_Wars:_Battlefront_II]Star Wars Battlefront II[/url]. As you kill enemies on a given map you can unlock a better weapon, and even unlock one of the Star Wars series characters (such as Boba Fett, or Darth Vader, or Yoda). The maps themselves never lasted that long, maybe 15 minutes or so. There is a campaign you can follow, or you can just do random maps, setting preferences for team sizes, time limits, etc.
I am not a huge FPS player, so maybe others will have better option, but i figured i would throw this out there.

I like UT GOTY best or UT2k4, also Painkiller is great fun.
Edit: If you don't mind some colorful language here are some level videos for Painkiller. I play it to make progress but also just replay levels for the fun of it . . lots and lots of critters to shoot . . .=)

I remember when both of my children were born that I actually stopped playing FPSes due to not really having enough time to really enjoy them. And at both times I ended up playing games such as GTA Vice City and San Andreas just for the sandbox worlds that they offered while also being able to save at almost any time.
Nowadays, I'd suggest something like the Avatar game or Red faction Guerrilla -- both action games that can be picked up and put down within minutes as required. Although they are third person perspective games.

The new Wolfenstein is a pretty solid choice. You get new Veil abilities, new weapons, and so on as you go through it. It's kind of open-world, because there are hub areas that you pass through while fighting Nazis. You don't have to worry about the story at all, because it's not something the game shoves down your throat, and you don't have to remember it to enjoy yourself. Despite some bad reviews, I found it to be a blast.

I'd recommend UT2004. Short independent matches, several different gametypes, tons of customization options and a metric fuckton of mods, mutators, maps, models and probably other things starting with M.

Well first of all: Congratulations!
Second of all: The game that probly suits your definition the most is Bet on Soldier. The game's kinda mediocre, but that is not a bad thing. It's fun, and it all revolves around fulfilling standard FPS-like missions, with the only little twist that are champions you meet while doing so. You are a champion yourself, and part of the environment becomes arena. I think you know what happens next. Anyway, for killing champions (you choose which ones you want to fight on the briefing screen for every mission - there's different reward for choosing different one.) When you win a duel, you get money for it, and you can buy a new equipment between missions to suit your needs.
Every mission lasts about 30 minutes in average as far as I remember, and even thou the game is unfinished in certain area and could be way more polished, it's just plain shooting fun, with no real story you'd need to pay attention to.
For more realistic games, I find Far Cry 2 to be a game to 'relax' - there's buying of new equipment to suit your play style and missions that will get repetitive over time - still, shooting stuff is fun, and the game's pretty atmospheric, every mission takes circa 20-30 minutes as well, including transportation to the mission spot. Again, there's no story that would really be worth keeping track of.
For really short and fun matches, there's always Unreal you have mentioned. I would recommend browsing for a bit and looking over the MODs - I'm pretty sure you'd find something that would shift gameplay precisely towards what you want it to be.

+1 for Painkiller. Completely mindless with zero plot, but great action.

Ha, I knew I forgot to include something. Yeah, Painkiller is a fantastic recommendation. Or Serious Sam HD, if haven't played the original one. ... And Duke Nukem :D

For shooters, I agree with the others saying Painkiller is a great game, with an outstanding atmosphere. There aren't some generic sci-fi levels coming after each other in a generic sequence, but very different scenes with an astonishing attention to details (some examples: an opera house with stage, balconies, backstage, a huge chandelier, marble steps and so on; a train station with corridors (including vending machines and ATMs), lobbies, trains, train schedules, "Wilkommen in Zurich" boards etc.; a dock, complete with cargo trains, cranes, loading bays, crates...). It can be quite time-consuming, though, with levels requiring 20-45 minutes to complete (not counting the time you spend redoing a part of the level several times because of some tough mosnters). However, you can save anytime you want, so maybe that's not a big problem.
Nexuiz is also a worthy candidate, where you can just jump in with a couple of bots for some mindless carnage. Also, it's free.
If you wish to heed bansama's advice, I suggest you buy Sacred Gold. It's an almost completely freeform Action-RPG (with moster scaling to ensure you can revisit areas you've already explored), which you can literally play for just some minutes or whole hours on end.

Haha, I thought by the thread title you meant you got a new dad and wanted to buy a game for him.
Congrats on the baby. :)
Gamers With Jobs may be a good site for you, also.
It's not a shooter but I find Street Fighter IV to be really good for short or long sessions.
Borderlands might be a good one. Shooter with lots of RPG elements (or RPG with lots of shooter elements, if you prefer) and not much dialogue, if I am perceiving correctly.
GOGs: , [url=http://www.gog.com/en/gamecard/expendable]Expendable, and another vote for Sacred...

every day shooter, geometry wars

On GOG: Painkiller
Elsewhere: Borderlands or Bullet Candy.

Fuck Far Cry 2. There's no relaxing in that. They stiff you with malaria, and it ruins the entire game. The game expects you to drop whatever you are doing when you run out of pills to do some tedious mission and get more. It destroys the open-world nature of the game, and it makes certain flaws, like the intersections that will always be stocked full of enemies, stand out even more.

Well, I see it's already been mentioned, but my first thought was Painkiller Black. It's easy to pick up and put down and lots of mindless fun. I was very surprised it was as good as it is. Runs great on nearly anything and you can play even 5-10 minutes or so and still have fun.