Whether it's your birthday, wedding or anniversary, you have a very good friend indeed if you receive a gift that you'd call "extravagant." In some cases, extravagance might have what some perceive as a negative connotation, but don't let perceptions or value dictate whether and how you adhere to proper rules of etiquette.
Saying "Thank You" is a Sign of Refinement
The way you say "thank you" demonstrates your knowledge of social graces. Also, it says that you're mindful of what others think about your manners and upbringing. Writing a personal thank-you note is the proper thing to do when you receive any gift, extravagant or not. Avoid writing something you believe is the modest way to handle receiving such a gift. For example, don't write, "You really shouldn't have spent so much on the gift." The person who gave you the gift probably knows he wasn't obligated to buy you anything, so don't insult him. Be gracious -- that's the key to expressing your appreciation for gifts, no matter how much they cost.