As long as it's established (AKA not purely in the realm of fanfiction), it counts. Crossovers are fine too, as long as it has been officially worked on.
You can visit each place for as long or short a time as you like. You can bring stuff back home with you, but if it wouldn't function by our laws of physics, it would fail, fall apart, or become simply decorative. People follow the same rules. You can choose to stay in one if you want.
Almsot all of mine are video game series, but yours can be from anything.
Mine:
Super Mario
Quirky, whimsical, lighthearted, and generally peaceful. And if the "acting troupe" thing is true, then things could potentially be even more peaceful. Might consider living here.
Pokemon
Goes without saying. Superpowered animal friends? Hells yeah. Also would consider living here, as long as I had plenty of 'mons to keep me company.
Star Trek
Life in the 24th century looks pretty cushy, all things considered. I'd love to try out a holodeck, mingle with all sorts of alien species, visit Risa, heck, I'd even consider joining Starfleet, as long as I was on the science or engineering teams! I'd want to stay away from border zones, though.
Legend of Zelda
In addition to the obvious (and doomed to fail) attempt to see Midna, I'd love to hang with Gorons or swim with Zora, explore the Lost Woods, visit the Castle Town bazaar, or see what lies beyond Hyrule's borders. I'd just have to make sure Ganon isn't due to rez during my trip.
Warhammer 40K
Just to sate my curiosity of how royally fucked everything is. I'd want to see a few IG tanks, maybe find a little trinket to show my allegiance to the Emperor, then run like hell at the first whiff of trouble.
Monster Hunter
Felynes. I love them. Also, I'd love to hear some war stories of some old hunters or go wyvern watching. Maybe I can partake of some local cuisines. I would love to try a Felyne-cooked meal! So tasty!
Elder Scrolls
I think I'd try to show up before the Thalmor screwed up the Empire, maybe before the Oblivion Crisis, too. Perhaps it's simply because Oblivion was the first Elder Scrolls game I played, but I'd really love to see Cyrodiil. It also seems to be the most diverse province, what with being the Imperial capital and all. I'd bring home some Surilie Brothers wine for my dear mother, as well.