I work at a university in Japan, worked at a different one previously, and was a visiting scholar for a year and a half at another one.
[実験室]{じっけんしつ} = a real laboratory -- as the term would be used in English. This is where you would conduct actual experiments in the natural sciences.
[研究室]{けんきゅうしつ} = either a professor's office or a room that students use to read books, study, goof off, etc.
[実習室]{じっしゅうしつ} = a room for practical training. As my university trains future teachers, these are rooms that look like classrooms. If it were say something like music, it would mean a music practice room.
To give an example, my friend is doing a PhD in fisheries. He and the other graduate students use a 研究室 that has their computers, books, and pet fish. From what I gather, his lab mates spend a lot of time watching hentai there. His advisor also has 研究室 which is his office as we would use the term in America. They have on their floor a 実験室 that contains several pieces of lab equipment including an HPLC.
See also my answer at Difference between 研究所 and 研究室