Blinkies are long, thin graphics, usually animated, that have a slogan on them! You can use them to convey your political standings, share your fandoms, or just be "so random lol rawr XD"
Buttons are similar, but a bit more stout. The typical dimensions for them are 88x31 pixels. The images on my Links In/Out page are buttons!
I first became aware of Stamps on deviantART. dA has (had?) a function where all you had to do to display the thumbnail of a piece on your userpage (or in a journal) was surround the piece's unique ID number with colons. (ex: :######:) If the image was small enough, it would just display the whole thing without shrinking it down. Much like Blinkies and Buttons, Stamps can proclaim your love (or disdain) for something. Graphically, they differ by having a scalloped edge, just like snail-mail stamps IRL.
You are free to display these on your own site, but you must include a link back to me! Either make the button itself clickable, use one of my site buttons, or include a clickable text link.