I was on a jury for a double murder case in 2007. You go through quite a bit: 1) Parts of court cases are very boring (mine went for nearly a month): Beyond reasonable doubt places a heavy burden on the prosecution, and they go to great lengths to prove even very minor elements of a case.
2) People run different agendas in the jury room: There can be a fair amount of animosity amongst jurors. Also you're in quite a confined space (the jury room) for long periods with 11 other people.
3) The experience wasn't particularly enjoyable, but it was interesting and I did feel I'd done the right thing by being part of it and a sense of satisfaction at the end.