I'm studying abroad right now in the Netherlands. It's not as common as in undergrad but you can definitly do it. I chose a school that had several study abroad programs (BU), but even if your law school doesn't offer anything, you can probably work it out with them to go abroad through a program offered at another school.
You can also do an LLM degree in a foreign country after law school. I think those usually take a year.
I know someone that interned abroad during their first summer of law school too. I don't know much about that other than the fact that it's possible.
If you're interested in reading more about my study abroad experience in the Netherlands - I'm writing about it over at http://andrewsinclair.org
. I just got here a few days ago so I haven't started class yet, but more reports are coming soon.