Sending out thank you notes is definitely proper wedding etiquette. The purpose of doing so is to acknowledge each attendee for actually coming to celebrate your big day with you and often times, bring a gift as well. It is a definitely token of appreciation as though it is your day, and your attendees were happy to come, they still made the effort and be there, and without them your wedding definitely wouldn't have been the same.
As far as gifts go, it is polite and definitely necessary to say thank you after you receive a gift. People don't have to bring you gifts, it is just a nice thing to do. This means that if you have a bridal shower, bachelorette party, etc. where gifts are given, thank you notes definitely need to be sent after each one of these occasions. To make it easier, designate someone to write the list of who purchased what present to ensure each person gets properly thanked for their present to you two!
It is just plain rude to not send thank you notes and if you think that your guests won't even notice, well you are pretty mistaken then. Guests will definitely notice that you never took the moment to acknowledge their presence and you never said thank you for the gift you purchased for them. Everyone will be happier if they receive some sort of acknowledgment!