I still use them, and they work really well for me! (I work at a credit union, and we provide American Express Travelers Checks for our members.)
Here's why: I usually travel with friends, and share a room with someone. It doesn't work to charge things to the room, since it would be hard to keep track of whose expenses are whose. It's simpler to get travelers checks in large denominations ($50s) and use them as needed to pay for meals, souvenirs, etc. I usually just carry what I need for the day, and keep the rest in the hotel safe. Also helps me keep track of what I'm spending.
Another reason is that if you lose travelers checks, you can call AMX and get replacements. Since I pulling out my credit card all day long, I'd worry about losing it (which is a huge hassle!). I use my credit card just to pay for my portion of the room, and pretty much use travelers checks for everything else.
I never use a debit card when traveling because if you lose it, someone can wipe out your whole bank account if they find your debit card! I use my debit card all the time at home, but worry too much about it when I travel.
As far as using prepaid cards (like prepaid Visas or Mastercards), I have had experiences when the card didn't work for some reason. Then what would you do??
Hey, it may be old-fashioned, but travelers checks work for me!