The only people I quote tend to be media people who have said something that really made me laugh, and then I tell whoever I'm with what they said (and they usually laugh too).
Other than that, I'm not a big one for quoting because I enjoy language and coming up with my own "quotes" (I guess they're not "quotes" if we think them up ourselves, but you know what I mean). For the most part, one of the things I think are most important about communicating with, and relating to, people is to come up with our own, un-recycled, thoughts.
A lot of people (including me) enjoy reading really good, meaningful, or funny quotes; so I might share a list or book with someone else. I just don't use them as party of my own conversation (and only very rarely use them in my writing). I guess I think there's a big difference between sharing someone else's wisdom and borrowing it for my own purposes and use in my personal communications with other people.