Hi Sarah,
Yes, we are starting to be able to detect sunspots on other stars, although not nearly as well as we can on our own.
As far as I know we can't make regular images of them, although sometimes astronomers can figure out about how big they are and their locations.

Here is an example scientists studying a star and finding spots. They were not actually able to image the star, but they can figure out about where the spot must be.
http://www.windows.ucar.e...arch_navigation.html

We can tell that other stars have sunspot cycles like our sun, although those cycles can be longer or shorter than ours.
Stars cooler than our sun are actually more active than our sun - they have more area covered by spots and have bigger flares.

cheers,
Terry