Chess Analyzer?

Nothing free but Fritz11 Has a game analyzer built in, pretty good one too. I use it when I start an analysis

There are a few free chess engines and a free GUI called Arena.  Some of the free chess engines are freakishly strong.

I don't think the free ones will just pop out a completely analyze game for you (I may be wrong) but you are better working in conjunction with the computer then just letting it do all the work for you.

Scid (free, Open Source) does this just fine. It can load and save PGN, and annotate a game using an engine. It includes several engines, and you can also use the free version of Rybka with it.

you have to do that manually. Its not like the computer will say "This is a bad move. What you should have done is BLAHBLAH or BLAH like in the game BLAH versus BLAH, Madrid 1998."

It may show you a line like the BLAHBLAH above, but without all the commentary. That is what YOUR brain (or a teachers brain) is for/can help you.