Are there any good sites out there that have a lot of these types of problems that are asked in interviews? Sites like http://spoj.pl seem to have problems that are more longer form. But it would be fun to start practicing solving the shorter ones that are asked without the hassle of interviewing to get them.

Other programming contest sites are good sources of problems similar to the ones that come up in interviews.

http://train.usaco.org/usacogate

http://community.topcoder.com/tc

http://uva.onlinejudge.org/

http://www.facebook.com/hackercup

http://code.google.com/codejam/

http://codeforces.com/

http://www.interviewstreet.com/recruit/challenges/

http://projecteuler.net/problems is a nice source