Things that are interesting and native to their culture. My wife collects key chains and since I would often travel I would buy them for her. I must say it is very interesting to see the differences between their cultures.
Personally, I enjoy collecting hats. You can wear some every day if you like, but, some cultures hats seems outlandish to visitors so those are more of just a story. This story may go into the origins of how they came about. It is facinating to learn so much from just a small item.
My wife and I will usually gather spices or jellies (jams). We love traveling to the islands and bringing back seasonings to use in marinades and cooking. Jerk seasonings and guava jellies are a couple of our favorites.
I'm a big coffee drinker, so I love mugs. But, I usually try to avoid the typical touristy souvenirs (the mugs excluded of course). I like to buy something that culture is known for or that you can only get in that particular region.
For me it's usually just postcards. I did buy some belts once in Italy but that was more an exception than the norm. My wife will bring back items that are of local interest to the area we are visiting such as wine or olive oil.
When my family and I drove cross country a couple of years ago, we decided to keep our souvenirs simple and purchased patches. Every national park we visited had a patch. It is on my "to do" list, but I am going to make a denim quilt and attach the patches that we got on the trip. That way I have something that I will use that will remind me of our adventures and not something I have to dust. On the trips I have taken to a foreign country, I pick up a locally made piece of pottery to use in my kitchen.
My top choice is local food. I usually try to get something which is easy to bring across immigration and will not spoil easily. Food is one good way to introduce a foreign culture to your friends too!