What are these buttons called?

Those are called antipixel badges or antipixel buttons. They're also known as brilliant buttons or steal these buttons.
Originated by antipixel.com and popularised by gtmcknight.com, 80 x 15 buttons are quickly becoming a web standard as their popularity rises among big blog owners and other web enthusiasts.
They're typically only 80 pixels wide by 15 pixels high and have been floating around since late 2002.
They're also sometimes called "chicklets" -- not to be confused with Chiclets, of course.
Other than just calling them buttons - I believe they could be a form of Userbars, however I cannot find a definitive definition of a Userbar.
Badges, I think. Wikipedia calls them web badges.
For some reason I seem to remember seeing a different name, way back when I was hunting down ones to put on my website, but I can't remember it now. (In case anyone asks: it wasn't "chicklets")
You could use those for other purposes than buttons. You could simply use them as "designed for: " notes on a page. You could simply use them as pictures for some reason or another. And anything else you can think of. I think the official name would depend on the use.