As someone who LOVEs to cosplay, personally the biggest thing for me is just the making of the costume. I love to sew, and create stuff and cosplaying is a really good way to achieve that.
Also on that note, at conventions and what not a lot of people pay attention and admire the work that people have done. So for people who are a bit of attention whores like myself it is a good way to get that sort of attention.
I am also a furry, and do the cosplaying there for similar sorts of reasons. The costuming is just so darn fun, and the challenges and what you work on for a fursuit are COMPLETELY different for most other costumes, it is kinda nifty actually. Though I am not happy with my first one, and am going to need to remake it, which is going to be WAY too much time and money, but hopefully the end result will be worth it.
This is a pic of me for a con a little while back, I made the fan my self, put a bunch of time into it and am REALLY happy with how it turned out.
I am thinking for some con in the near future of doing a TF2 cosplay, but I am not sure which I want to do. I am debating doing a medic or soldier, but I am not sure.