All Participants Work For The Benefits Of The Project

Most people hate to work in support, because they are tired of all these stupid clients, who doesn't understand at all how things work.
Some people even hate to explain something to their colleges: they think that colleges wasting their time by asking questions that they probably could just google. I've found a quiet simple solution for myself to reduce this kind of feeling:
All participants work for the benefits of the project
Basically, every time I feel "oh, that stupid question again" I remember, that it isn't about me, it's about the project. And the project definitely benefits if I answer on this question reasonably and exhaustively.

It helps even in the tester-developer situations: there are some developers who don't take testers seriously. And only reasonable thing that you can do in this situation is to show that testers are useful too. And one way to show it is to help developers (for example, testers can help to update versions, update/write manuals, create test data etc).
Help your developers!
It also helps in situations, when you feel "it's not my work, I don't want to do that". In the scope of project it doesn't matter who did something - it matters that something is done.