If we are with the gift giver when we open the gift, then no we don't. Otherwise I do and I have my 3 boys write them also. In fact, I won't let them use the gift card, cash the check, etc. until a thank you is written. I do allow the boys to make a phone call or send an email (if appropriate) rather than write a note. I have always told them that if someone take the time and money to give them a nice gift, a thank you needs to follow. It may be an old-fashioned way of thinking but I feel it's very important.
The boys are now 20, 16 and 14 so I can only hope this is something they'll continue to do on their own.....