Depends on the kind of whale, as you thought. The record diver is probably the sperm whale, which has been timed as diving for two hours. Sperm whales also hold the dive depth record, since they've been tracked to more than 7,000 feet and there's good circumstantial evidemce that they can go deeper than that.
Beaked whales are also long, deep divers.
Dr Bruce Mate of Oregon State University has had a satellite tag on a humpback whale for around six months now, I believe, and that's probably the record. It is only ever given for research or public display purposes. Well, we don't know in all cases, and there are probably different reasons. Single whales that come up do so because they are very sick. Thank you for answering my questions, I really apreciate it.