How to remove multiple blank lines from a file

I have some text-files I use to take notes in – just plain text, usually just using cat >> file. Occasionally I use a blank line or two (just return – the new-line character) to specify a new subject/line of thought. At the end of each session, before closing the file with Ctrl+D, I typically add lots (5-10) blank lines (return-key) just to separate the sessions.

This is obviously not very clever, but it works for me for this purpose. I do however end-up with lots and lots of unnecessary blank lines, so I'm looking for a way to remove (most of) the extra lines. Is there a Linux-command (cut, paste, grep, …?) that could be used directly with a few options? Alternatively, does anybody have an idea for a sed, awk or perl (well in any scripting-language really, though I'd prefer sed or awk) script that would do what I want? Writing something in C++ (which I actually could do myself), just seems like overkill.

Case #1: What I need is a script/command that would remove more than two (3 or more) consecutive blank lines, and replace them with just two blank lines. Though it would be nice if it also could be tweaked to remove more than one line (2 or more) and/or replace multiple blank lines with just one blank line.

Case #2: I could also use a script/command that would remove a single blank line between two lines of text, but leave multiple blank lines as is (though removing one of the blank lines would also be acceptable).