The Czech Republic, where I'm from, is a land of tourism, hiking and coming up with various systems to improve and gamify them. We are quite the active Geocachers, heavily use the Czech Hiking Markers System, and among other things, we have a plenty of different collectables for grabs at interesting destinations.
Personally, I like the occasional trip, and when I take it, I make sure to get rubber stamps prints and Wandercards. The stamps are wonderful on their own (free, creative, fun – you never know what design you'll run into), while the Wandercards give me a commercial complement that's pretty to look at and rather easy to store. Also, I find their "reward system" to be the most interesting.
And now, for a non-exhaustive list of what kinds of these collectables there are:
Turistické známky (Memory Stamps) – thick wooden medals engraved with a laser. They come with a coupon with a stamp-specific number; if you collect a sequence of ten numbers, you can mail them in for rewards.
Turistické vizitky (Wandercards) – sticker "visiting cards", to be collected into a specialized diary. They always come with two smaller stickers: one to put into the diary's "index", the other bearing a code you can eventually mail in for rewards. Some have extras as well: I've seen photos, miniaturized maps, +1 entry coupons to exhibitions and small information sheets. As for the diary, you can use it for other collectables as well; it even comes with extra pages.
Turistická razítka (stamps) – similar to passport stamps, non-commercial, non-centralized (rubber) stamp imprints of various designs and colors. You can collect them in any diary you want.
Turistické magnetky (magnets) – many varieties exist, some non-centralized, some centralized, some even with reward schemes of their own. The household fridge is probably the most popular place to display them.
Turistické štítky/odznaky (tags/badges) – small bended metal plate badges with a colored front, intended to be either collected normally or hammered onto a wooden walking stick
Pohlednice (postcards) – self-explanatory. There's also a line of collectable postcards named "pidifrk".
And more...