Souvenirs are one way to remember a place you have visited. Most tourist sites have countless items for sale, but of course you aren’t limited to what is in the various shops at your destination.
I have friends and family who collect things like shot glasses and spoons from various destinations. Another collectible that seems to be popular are Starbucks mugs. There are city-specific mugs for sale in most Starbucks stores. Not my thing, but it can work as an easy memento for the last minute shopper due to the prevalence of outlets in airports. (see above)
For all of my travels, besides taking photographs, there is not one thing I collect at every destination. I often end up with coins from foreign countries, but I don’t usually make a conscious effort to collect them. In recent years, I have been keeping hotel keys, and I make an effort to keep card stock boarding passes for my more interesting trips as a permanent record. I also find myself buying oddities that aren’t usually easily found at home, and often times give them as gifts to friends. Things like Darlie toothpaste from Hong Kong or Thailand. (This is very non PC, particularly the former name and packaging). I also remember buying a bag of almonds in Taiwan branded “My Nuts”. Apparently my sense of humor stopped maturing at age 14 or so.
I’ve also bought postcards when traveling, some to keep, and some to send to my young nieces. Some of my fondest travel related memories from childhood include the postcards my grandmother sent from her journeys around the world. I certainly don’t send as many postcards as I used to, since electronic communication is much simpler, but I still enjoy sending (and receiving) them.