I guess no one leaves Thailand without doing anything with elephants. I mean, elephants are for Thais what cats and dogs are for the rest of the world. From souvenir items to football games, from T-shirts to temples, the Thais have probably cornered the international market for elephants.
For the more adventurous (or the gullible, depending on your bias), the best way to appreciate Thai elephants is to take a ride on its back and traverse mudfields and rivers during the course. The ride is a bumpy one (my friend Pam's screams and bleep-bleep comments toward the end prove that) but you can never ever fault it ever for being not memorable.