Looking at this topic from Long and Short Reviews, there was only really one answer to give. I've been a collector of a lot of things over the years - I used to collect keyrings as a child, and had a huge bunch of them before I was forced to throw them out when I left home - but I have one thing in particular I've been collecting for the last few years.
Autographs. Occasionally via eBay, but primarily through writing to celebrities.
The above is one of my Holy Grails. Gene Wilder was well known for being difficult to get unless you jumped through certain hoops - you had to provide your own photo, mention more than one thing you'd seen him in (no hardship there, I loved his work) and add that you knew he was a very busy man, otherwise you'd get a pre-print and a note about how he was too busy to sign. I managed to get it right, and the above picture was the result.
I have also bought autographs by way of celebrities' websites, such as the Felissa Rose one above. These are better than going via eBay since you can pretty much guarantee they're genuine and you can also get them personalised, which is a win for me since I'm never going to sell them.
So what do you collect?