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 active Geocachers, heavily use the Czech Hiking Markers System, and we have a plenty of different collectables to grab at interesting destinations, among other things.
Some of said collectables include:
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...
As long as I have places to visit I do like the rare trip, and when I take it, I make sure to grab 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.