It will work with other routers, but only on a basic level.
It can't do range-extending without an Airport Base Station, that much I do know. I tried to get it setup like that with my Linksys WRT54G and no dice. It'll only act as a client.
I think there are a few other nicities you lose if you don't use with an Airport Base Station, but the range extension feature is definitely the one I miss the most.
And it will certainly act as a full-fledged router if you'd like to use it that way. It's also worth noting that their range is surprisingly good too.