Earth - Hubble is moving too fast to get decent close-up imagery, the distance is too small, and frankly Hubble just wasn't designed for it (as opposed to spy satellites of the major powers). Hubble does use the earth to calibrate its cameras, though.
Randall gives examples of how imagery might turn out.
Moon - speed's an issue, but less so, especially if you're imaging a large region
https://what-if.xkcd.com/32/
Earth - Hubble is moving too fast to get decent close-up imagery, the distance is too small, and frankly Hubble just wasn't designed for it (as opposed to spy satellites of the major powers). Hubble does use the earth to calibrate its cameras, though.
Randall gives examples of how imagery might turn out.
Moon - speed's an issue, but less so, especially if you're imaging a large region
Here's an example: http://hubblesite.org/newscenter/archive/releases/2012/22/
Mars - Hubble has targeted this planet lots of times.
Some examples: http://hubblesite.org/gallery/album/solar_system/mars/