I have always been a bit of a rebel when it comes to awarding experience. My normal method is to just pick a number that seems right, based on how much I feel the party accomplished. I keep a log tracking how much experience I have given for past sessions, along with a one or two sentence reminder of what the party was up to. I compare what just happened with previous sessions and look at what I awarded in the past, and this normally makes it easy to tell how much XP to award. Part of the reason I have been doing this in my Mutant Future campaign is that I rarely give out "treasure" of the normal gold piece, silver piece, etc. variety. I don't really see there being any sort of money economy in my world, barter being the rule of thumb, but this lack of gold means that if I gave out experience by the book, the players would advance at a glacial rate (because Mutant Future uses the GP for XP rule).
As I mentioned in my post about hit points in the Mutant Future, what level a character is does not make as much difference in this game as in regular D&D. A character's HP are always going to be more or less the same, and what mutations a character has is arguably more important than the level attained. In this respect, I guess it really wouldn't matter if the characters took forever to level up. But on the other hand, this also means that there is no reason NOT to level up characters fast.
I recently started a campaign wiki of sorts (actually just a blog that I have given the players administrator privileges to). I have been awarding experience to players who post on the blog between sessions, at the rate of 100 XP per comment and 500 XP per new blog post. This means that a character could level up between sessions if the player posts enough!
So far, this idea has been working well. Players have posted everything from new Mutant Monsters to wishlists for the Mech suits that they want the Mice of the Round Table to build for them. One benefit to me as a DM is that the players have taken to discussing strategy and plans for the next session. This means that I can do prep work with greater certainty that I am not wasting my time readying something only to have the players do something entirely different.
Questions for my readers - How do you award experience? Have you ever given experience for something that occurred outside of play?