This is for those with trouble understanding spoken English due to various reasons; hearing problems, deafness, not being used used to spoken English, broken speakers/headphones, sound turned off to not wake the roommate, whatever...
Not only for listing subtitles, but also for games where audio is not necessary to play (many strategy games should fit there). Please help in filling this list.
For those of you who'd rather play games in your own language, I can recommend the list of multilingual games.
::: GOGs (the main reason)
Arcanum
Beneath a Steel Sky
Fallout
Fallout 2
Gothic
Gothic 2
::: GOGs without subtitles
The Feeble Files
::: Not-yet-GOGs (since people mentioned them)
Bioshock
Batman Arkham Asylum
Devil May Cry 4
Dragon Age: Origins
Fallout 3
The Witcher
::: Not-yet-GOGs without subs
Assassin's Creed
Singularity

Rep given for this!
I'm profoundly Deaf myself... And I notice a disturbing trend towards fully dubbed games nowadays... Not good.
Anyway, I'm currently playing:
Bioshock
Batman Arkham Asylum
Fallout 3
Dragon Age: Origins
And all of them have FULL subtitles for everything....
Another few off the top of my head:
The Witcher
Devil May Cry 4
Hmmmm.... Cant think of more atm.

I think people needing subs in games or having hearing problems might look there
http://www.deafgamers.com/
they have a great list of games that you may look for and with reviews centered around your hearing problems
Hope it will be of help to you

Subs are pretty standard these days but there are some exceptions indeed.
The biggest and most annoying one is the first Assassin's Creed that features no subs at all.
Singularity had none too.

Oh... didn't think of new games at all, with my other lists being very GOG-centered I thought it'd be clear this one was also meant GOGs. Heh.
Oh well, I'll fill in those not-yet-GOGs as well.

Arcanum and The two Gothic.
Many other too. I will write them later.

To be honest I find www.deafgamers.com a pretty... well, crap place.
Their reviews just don't do it for me. *shrugs* Just my 2c