I am a beginning indie developer, and I want to get the word out about my game. What sites can I go to to ask about reviews of my game, and where might I be able to talk about and get feedback on my game from players?
The answer will really depend on what kind of game you've made. Here are some of my thoughts:
For Flash: Flash Game License is a good place to get feedback from other developers, you could also try Mochi's forums. The FGL people also run Flash Game Distribution which can help get your game out to different portals (if you decide not to get an exclusive sponsor). This answer has a good list of portals you could submit your game to.
Generally: Sites such as the Indie Game Blog and TIGSource might review your game if you send them some info. The TIG Source also runs forums where people can play your game and leave feedback. The Indie Gamer forums is another community which can help.
I would send (and have) an e-mail to every single website out there that reviews games of any kind. But not before I have an almost completed game. Be real. Be humble. Show off something innovative.
A lot of places won't really take their time looking at you until you have something put together. Don't try to approach reviewers to review a pre-alpha-alpha prototype. It might sound like common sense but I have read reviewers make that kind of remark (which is enough of an indicator).
As for feedback. Grab a few play testers, preferably locally, that you can watch play your game. That will be some of the best feedback you can get. Alternatively, follow the other's advice. tigsource.net, gamedev.net and devmaster.net forums.
Both Bytejacker and Rock, Paper, Shotgun have a sizable readership and will review indie games sent to them if they find them interesting enough. I also second Alex's idea of the TIGSource forums; just make sure you follow their guidelines for new users and post in the appropriate category.
My advice is to know your market. A mud for example, usually buy ads on topmudsite or mudconnect. An MMO might want to buy an ad at massively.
Indie game developer probly could get some good publicity by being upfront and simply posting at an related forum saying that they have a new game and want people to check it out. If you do this however, dont be pretentious and say you found a cool game and want people to try it. Just say that you are the developer and hope people give feedback on it. Try to find a genre specific forum for this. For example the wargamer forum is a nice place to do this if you have a grognard-ish game. Gamedev forum is also nice for this, but targeted audience is always better.
Find blogs that post about games/apps of what you are developing for. For instance, if you are creating an Android game, then first I would get some sort of PR statement about the game together for blogs to post (with some screenshots of the game or video! A must!). This is even better if you have a website you can put this out on. Then hit up every Android related blog and see if they'll write a review for your game. Most of these blog sites also have forums that you can post to about your game's release.
You can easily replace "Android" for "iPhone" or "xBox" etc.
I posted this answer in a similar question
I don't know how effective this idea is (I haven't tried it yet) but for my current project I am going to advertise on Facebook. Let me explain.
Essentially I am going to create a fan page, and run an ad campaign on Facebook. What I figure is I can spend like $30/mo (or what ever you want) for advertising. As people become a "fan" of the page, a lot of other people will see that. So basically, if that $30/mo generates 5 fans directly, it could generate 50 fans indirectly. I figure I could also do some fun stuff with the fan page such as give away copies, solicit ideas, etc...
Like I said above, I haven't tried this so I don't know if it will work. However, I will let you know in the near future. :)