There's only a couple new finds today, but I have a bunch of older songs that deserve to be mentioned so I'll go through most of those.
Also, for all of the videos that I link here, I download them and extract the MP3 or AAC audio from them. If anyone's interested, I might start zipping up the songs from each post and tossing them on RapidShare or something for people to download.
アンインストール (Uninstall) [Nico Nico]
This is a cover of the anime Bokurano's OP theme and the song that first got me hooked on Hatsune Miku. Both the original song and this version are incredibly beautiful and it's since become one of my favorite Japanese songs, even though I've never actually seen Bokurano.
きっとこの場所で (Kitto Kono Basho de / Surely in this place) [Nico Nico / YouTube]
One of the first original Miku songs that I really fell in love with.
恋は戦争 (Koi wa Sensou / Love Is War) [Nico Nico / YouTube]
Another simply amazing Miku original.
メルト (Melt) [Nico Nico / YouTube]
And yet another, though this one is a little more cheerful. Also, the YouTube version has a nice 3D video to go with it.
ブラック★ロックシューター (Black Rock Shooter) [Nico Nico / YouTube]
Okay, just do yourself a favor and visit this site. It has links to these last three, plus World is Mine, with some extra stuff like wallpapers.
After The Rain [Nico Nico]
I really like the distortion (I think that's the correct term for it) on the guitars in this one.
books [Nico Nico / YouTube]
A beautiful piano piece that slowly builds momentum from a gentle start.
Rainbow Girl [Nico Nico / YouTube]
There's some nice art of Miku in the video for this one.
Caramelldansen (Speedycake Remix) [Nico Nico / YouTube]
You all knew it was coming. The combination of Miku plus Caramelldansen is too cute for words so I won't bother trying to describe the awesome of it. But, for those who don't know, the original version is by a Swedish band named Caramell, and Caramelldansen translates to, "The Caramell Dance."
Heaven Is a Place on Earth [Nico Nico / YouTube]
I'm a fan of Belinda Carlisle's music and this is a cover of her most popular song. Miku singing in English is always funny but they did a pretty decent job of it here.
Eternal Green [Nico Nico]