Check out Theta Music Trainer .
Lots of games for ear training and music theory.
music.stackexchange.com/users/1363/emm2005
Technically, I think the vocals portion of Rock Band counts for this, as would its precursor SingStar.
If you've got a Mac and a familiar iTunes library, my friend made this game, almost as a joke.
(It plays back x number of tracks from your iTunes library simultaneously until you identify them...
it's called " Counterpoint .")
That could feasibly train your ear in an abstract sense, since you're essentially trying to pick out familiar musical snippets from a very dense soundscape.
Ooh, Legend of Zelda: Ocarina of Time had a game mechanic centered around playing back melodies on your N64 controller-turned-ocarina.
Ah, also Ambrosia Software's game Aquaria (also available on Steam) has a similar game mechanic that provides you with a diatonic scale from which melodies can be sung.
music.stackexchange.com/users/133/NReilingh
You might be interested in GNU Solfege .
It's not a game per se, but it has A LOT of exercises with visual and aural feedback.
It also records statistics about each one of your performances, so you can know how well you're learning and "score" yourself.
I've been using it for some weeks now, doing a few exercises each day
and I can say it is lot's of fun and very didactic as well, but your mileage may vary.
music.stackexchange.com/users/1186/lfzawacki
Looks like you received a bunch of great answers already, but I thought I'd add something to the list anyway.
Have you tried: TENUTO (App) -
It has a great set of Games/Tools for Ear Training and/or Sight Singing (VERY helpful, even if you never make a sound) http://www.musictheory.net/products/tenuto 8 NOTES
(Online/Free) -
The WebSite includes 10 games, some are GREAT and they're ALL free!
http://www.8notes.com/games/
music.stackexchange.com/users/3102/Chris Morriah
I've never used it, but Sibelius has some ear-training software called Auralia which is supposed to build your ear up using training and games.
music.stackexchange.com/users/175/BlueRaja - Danny Pflughoeft
There are simple ear-training games in Band-in-the-Box .
Those are quite simple, but even fun :)
The first is called Music replay game.
It has three modes:
note, rhythm and melody replays.
The computer plays note or phrase and you have to replay it using a computer keyboard or midi instrument.
You can set up a tempo and range of notes.
There is notation displayed too, so this can be a sight-reading game too.
Second is the Pitch Invasion - this game has the same controls and set-up possibilities as previous one.
There are flying saucers falling down and each of them projects a audible pitch.
By guessing it, you shoot the saucers down.
This game is great for children.
music.stackexchange.com/users/874/Hubert Czerski
There is the good old LOOM
This is an adventure game.
The game requires one to memorize spells in the form of short tunes of 4 notes.
To cast a spell one needs to play back the tune.
Depending on the difficulty level it is done solely by ear or with a written notation.
Some spells can be played backwards reversing the meaning.
Changing, for example, open to close .
music.stackexchange.com/users/1496/horsh
Check EarMaster Pro 6 its not free
but we can have 7 days full trial version.
music.stackexchange.com/users/3235/Bala Krishnan
There have been several popular music games in recent years, but they seem to be most useful for developing a sense of rhythm. Are there any games that are helpful as ear training exercises? What would you recommend?
Are there any games useful for ear training?
music.stackexchange.com
<ear-training>
music.stackexchange.com/questions/209
music.stackexchange.com/users/136/Brian Slesinsky
Games for training the ear include Theta Music Trainer, GNU Solfege, TENUTO, Auralia software, LOOM, Earmaster Pro 6 Here are some suggestions for ear training. Theta Musica Trainer, Rock Band, SingStar, GNU Solfege, TENTUTO, Sibelius, Auralia, Band-in-the-Box, Loom or EarMaster Pro 6 
Here are some suggestions for ear training. Theta Musica Trainer, Rock Band, SingStar, GNU Solfege, TENTUTO, Sibelius, Auralia, Band-in-the-Box, Loom or EarMaster Pro 6 