"Indie" is short for "independant" obviously, but beyond that the term is a bit vague and may mean different things to different people. Generally, it means that the studio is not dependant on their publisher or any other outside party.
My rule of thumb: if the publisher funds the game or gets to own the copyright instead of the developer, then it's not an indie game.
In my personal opinion: yes. It's an unusual case, since Valve just happens to be a big publisher in their own right, but that's an outgrowth of them self-publishing to avoid being dependant on VU.
(edit: Yay! 100 Rep!)

I found this game aswell:
http://store.payloadz.com/details/229037-Software-Games-Quest-of-Persia-Lotfali-Khan-Zand.html
The only Indie game which made it outside of Iran.
I got curious and bought it since I never saw any reviews of this game and gave it a shot.
Now I fucking regret it. The game is DRM'd with a screwed up key check system. Also the download option is not unlimited, it will go off in an uncerain period of time.
Of course, I installed it and got a manual of the game, supposedely there should be a serial number for unlocking the option to enter your registration key which allows you to open the activation key. And there isn't any serial.
FUUUUUUUUU
I sent them an email for support, once I can get the key I am gonna fucking send them such a long complaint about DRMs. They already released a sequel to this last year and it's supposed to get released internationally aswell:
http://www.youtube.com/watch?v=S0L7uAFWfwI&feature=related
Goddamn newbs, I hope my money doesn't go into some bank account of some mullah.

Gang Garrison 2
Pretty fun demake of Team Fortress 2. I got addicted for a while. :(

Not really new, but Eversion is now available on Steam. I don't know whether it's still freeware elsewhere--I'm buying it anyway to support the developer.
For those of you who still haven't played it, don't read up on it or watch any videos of it before playing. All you need to know is that it's a pretty great 8-bit-style platformer. The rest you should discover for yourself.
Edit: Apparently still available at the developer's website.

Dammit, if GOG starts selling new (indie) games for an accessible price, I'd buy almost all the titles mentioned here.
That's a nice URL. :)
And I'll look for this game, looks good and old school-ish.
"Eversion:
The Princess of the Flower Kingdom has vanished! She was taken by the Ghulibas of the north, and it is up to brave Zee Tee to rescue her. On his quest, he - and you - will discover the hidden lands behind the peaceful kingdom, and come face to face with secrets that will set you on edge!
This is the high-definition version of indie fan favorite Eversion, now with Steam support! Complete achievements and compete against your friends in Time Attack levels!"

If you're considering the Eschalon games, I'd say go for it. They're great fun, well worth the money, and they're also DRM free. So no need to wait for GOG to pick them up if that last is a concern.

Looks like you know my game preferences. ;)
Indeed I want Eschalon, and I want Din's Curse, the Introversion's collection, Galcon Fusion, and others indie titles of a higher profile, if you get me. Not flash games converted to an exe.
I'm fine with purchasing directly from the devs (but only if it's drm-free), the thing is that I'd like to concentrate my collection of games in only a few sites, not 20, not 200 sites.

Understood. It can certainly be more than a small pain in the backside if you're dealing with a ton of different sites for your games.

There is an actually surprising good game :
http://www.longbowgames.com/hegemony/
If you liked Knights of Honor or Total War games (in a certain extent) this one may be worth a try. Something that I could call a cross between STR "fun" and wargames "seriousness" this means you need to plan supplies and campaigns in order to wage war but it also means that all this management is rather simple compared of what can be seen in wargames. The game has several objectives that won't let you get lost in all the possibilities but you can select them as you wish.
A special note about the publisher stance towards DRM : They're absolutely against DRM and even allows you to re-download the game from thier site if you bought it on Steam/Impulse/etc... plus the whole thing is quite cheap.

http://www.blendogames.com/
All of his games are short but are fun.

I've opened an entire thread about it because I think it deserve it :P
http://www.gog.com/en/forum/general/a_new_old_game_for_you
http://www.bohthegame.com/

upcoming
Evochron Mercenary