I completely agree with you about the soundtrack to a video game really making it what it is, and I'm also a big fan of video game music. However I have considerably less experience when it comes to freeware, all of my recommendations are gonna be consoles.
Shadow Of The Colossus
Revived Power-http://www.youtube.com/watch?v=qR_s3BGLu0s
Classic exhillerating baddie-stomping music.
A Violent Encounter-http://www.youtube.com/watch?v=fUuo_PfcxN4
More of the same. I'd recommend the whole soundtrack, it is all fantastically grand. It won an award a while back.
Parappa The Rapper
Live Rap with MC King Kong Mushi-http://www.youtube.com/watch?v=0s7cntB6ljQ
Feel good pop. Insanely catchy, you will be humming this.
Chop Chop Master Onion's Rap-http://www.youtube.com/watch?v=nJ3o3kQZWm8
Jet Set Radio Future and Jet Set Radio
Jet Set Medley Future-http://www.youtube.com/watch?v=JF7JJBiYn-s
Both games have this electricy sythy rappy feel, and the funky tunes just add to it.
The Concept Of Love-http://www.youtube.com/watch?v=9v3WlGg99oM
Future's title music.
Metal Gear Solid Series
It's come under criticism in recent years for being saturated with cut-scenes, the music always made them a pleasure
Encounter-http://www.youtube.com/watch?v=MEvv10M0JTM
Probably one of tracks most in sync with gameplay in all of videogaming, in my opinion. This plays in my head when answering the door to salespeople.
The Best Is Yet To Come-http://www.youtube.com/watch?v=6miaTf1gF4g
Truely touching. Almost cried after completing first game for the first time.
Can't Say Goodbye To Yesterday-http://www.youtube.com/watch?v=1m4tYUfYCj4
More touching stuff. The ending themes are always great.
Snake Eater-http://www.youtube.com/watch?v=9aHQnDTd1y4
Almost cliched how popular this track is.
Don't Be Afraid-http://www.youtube.com/watch?v=97AsoWWcKIY
Loved the 60's theme to the music in this game. Really enjoyable. I don't want to post more of the game, but I would recommend looking up Surfing Guitar.
Calling To The Night-http://www.youtube.com/watch?v=PXkgn3QUA2w
More soulful singing. Most known from it's inclusion in brawl.
Ace Attorney Series
Popular over-the-top courtroom drama.
Any of the Objection! and Cornered themes from across the series are good, but I'd say the best game music is from the third.
Objection-http://www.youtube.com/watch?v=lGvmGpt5678
Cornered-http://www.youtube.com/watch?v=9OlYy_TD19E
And alot of the music from this series has been reworked and re-recorded.
Special Blend Mix-http://www.youtube.com/watch?v=5iVO464_BbM
All of the music in this series has complemented gameplay so well it is unreal.
Katamari Damacy Series
Crazy Japanese Quirk.
Katamari On The Rocks-http://www.youtube.com/watch?v=hR7nX76eRiI
Katamari On The Swing-http://www.youtube.com/watch?v=WCngZZFG7r8 (This was playing in Travelling Man today, I smiled and felt less depressed with my life)
Katamari On The Funk-http://www.youtube.com/watch?v=9EQnzIT5STM
This is all upbeat poppy electro. It is also more horribly catchy than anything and makes for great whistling.
Overture-http://www.youtube.com/watch?v=rYD6e55jg1A
Overture II-http://www.youtube.com/watch?v=7G0pBGYXH34
Overture III-http://www.youtube.com/watch?v=C7DEL321NSk
Funky piano music. Go find the sheet music and learn to play these, it impresses girls.
Vib Ribbon
Polaroid-http://www.youtube.com/watch?v=tZ8MLs7J7KA
More trippy electro
I could go on forever (or at least a page). This is all great stuff in my opinion, I'm sure one of you will hate it. I'll work on the freeware, but I'm not promising anything.