I am an avid collector of live music ("bootlegs"). Here you can find some information about bootlegs, as well as my personal collection of bootlegs.
Philosophy
People argue that bootlegs somehow deprive artists of royalties. I don't agree. Bootleg traders (I can't speak for everybody, but I'm sure I speak for 99% of bootleg traders) do not see bootlegs as a substitute for albums. Nobody I know would seriously get a bootleg of an artist instead of one of their albums. Bootlegs are far less polished pieces of works than albums and the sonic quality is nowhere near.
Bootlegs are a complement to official releases - something you get after you've already listened to all a band's albums a hundred times. Most of the people who will collect a band's bootlegs are the die-hard fans who already own all their albums, probably most of their singles and a couple of T-shirts as well! Most of the traders I know will spend a lot more per month on official CDs and concert tickets than most of the non-traders, simply because bootleg traders are big fans of music.
Record labels sometimes argue that if they ever decide to release live albums, they don't sell very well because people often already have the bootlegs of the shows. In my experience this is not true - people generally stop trading a bootleg if they hear that an official release of the show is expected.
This has happened with Counting Crows' "VH1 Storytellers" and "MTV Live At The Ten Spot" shows when they were officially released as the official 2-CD live album Across A Wire. It happened with Guns'n'Roses's performance at the Rock in Rio festival. It's happened loads of other times too - too many times to list here.
Bootlegs can help increase a band's exposure. Bands like The Grateful Dead, Phish and Dave Matthew's Band would never have gotten as big as they did without their pro-taping policies.
Bands don't often release live albums. Bootlegs are a good way for fans to listen to live versions of their favourite songs in the comfort of their own house. Even if they do release a live album or two, it may not be as good as one particular show. You can't overestimate the joy it brings to relive a great concert that you've been to. Only bootlegs can bring this joy (unless the band decides to release every live show they've ever played!)
Bootlegs are a great way of meeting people. If you've been away from trading for a while, it can be great to get back into it. I've made some good friendships through trading CDs.
So there you have it - bootlegs are a great way to promote artists and a great thing for fans. And hey, if you're still not convinced, at least trading bootlegs keeps me off the streets.