There's a couple of different components to making good background music for a game. Try to avoid using too much functional harmony (cadences and secondary dominants stick out like sore thumbs). It's debatable whether or not a strong melody is useful. Games like Pokemon, Final Fantasy, et. al clearly have these heavy handed melodies (often the result of limitations of the early game platforms), but they managed to win the hearts of many. It's a balancing act when deciding to lean toward a more melodic or textural approach.
Another thing to think about with game music is dynamic structure. Depending on what tools and libraries the programmers are using for audio (and how much work they're willing to put in implementing your music), you might be able to take advantage of. FMOD (http://www.fmod.org) and Wwise (http://audiokinetic.com) offer a pretty robust visual authoring tool that acts as a middle man between composer/sound designer and programmer.
The two concepts that these tools build on are branches and stems.
Branches are the most basic type of musical structure for games--it's is what it sounds like, branching to another piece of music. This can occur on a higher level, such as changing themes between town and overworld or between levels, but you can also chop up your A-B-A piece into {A|B|C}-{D|E|F}-{A|B|C}. In that case, you'll have three distinct segments that could function as 'A' and three distinct segments that could function as 'B'.
The game code will choose one at random or based upon the current state of the game. In keeping with the {A|B|C}-{D|E|F}-{A|B|C} structure, maybe B and C are a little more upbeat, so if all the characters in the party have full health or the player hasn't died in a while, the audio engine might favor playing B and C over A.
Stems are like individual tracks. Imagine you're a DJ and you have a basic kick-snare beat. As you develop the tune/remix/whatever (disclaimer: I am not a DJ lol), you may fade in a melody track or a rhythmic texture track. A common technique for action games is to have a consistent melody stem, and then have an initial light percussion/bass/rhythm track crossfade into more intense variations as more enemies appear on screen.
With Wwise (or if the programming team rolls their own advanced music playback action), you can mix tese two approaches. Still have the alternate A and B themes, but then have those be made up of a set of stems that vary. Or, have plain stems, but them temporarily branch off to a transition segment so you can modulate to another key (listen to Tom Clancy's H.A.W.X., the composer structured the music such that for greater intensity levels, the music would modulate up a whole step).
The whole point of building up these dynamic structures is to not only provide variety, but to also provide variety that has meaning to the player.
Hope this was useful! Even if your team doesn't have the resources to do any crazy adaptive music stuff, then maybe this can at least help you think about structuring variety in your game tracks.
Oh and I'll throw my recommendation for game soundtrack listening in here: Bastion (http://supergiantgames.bandcamp.com/) :)