It has changed over time. When I was young, I collected action figures and lunch boxes - Star Wars, GI Joe, Smurfs, etc. In my 20s, I collected mostly sci-fi movie posters (I practically lived at Suncoast in the mall). My 30s was DVDs and McFarland collectible figures (oh how I miss Media Play!) In my 40s, I must actively stop myself from collecting ALL THE FUNKO POPS.
I collect everything Star Trek, of course - but I specifically collect Star Trek Christmas ornaments, which I proudly display every holiday season.
I have a collection of clothing and accessories from the 50s and early 60s. I adore that era and even used elements of the 1950s in my wedding. Movies, books, hats--- I love it all!
When I was a kid I had a huge collection of all things Garfield. I eventually sold it all but now as an adult I have started collect Garfield things again.
I also collected Garfield stuff when I was a kid!
When I was young, I collected international and vintage stamps, coins, geodes, rocks, solar system posters, miniature animals, porcelain dolls, pens, Baby Sitter's Club and Goosebumps books, and anything green. Then as grew up I realized I'd have to cart that shit around (and dust it)... So, I don't collect much any more.
(I also collected jokes and bad puns. I memorized tons of bad jokes and annoyed my family with them at every opportunity.)
I was a huge pencil and paper RPG player in college, and I have a pretty impressive dice collection - but I haven't been able to find it since we moved :( Every time I got really into a new character I'd go buy them their own set of dice :)