Tumblr user PhemieC has some great filk; it's mostly Homestuck but lately it's been a smattering of other fandoms, such as Dragon Age, Ib, and Hannibal.

http://phemiec.tumblr.com/tagged/music

If you want catchy Doctor Who-themed songs, look them up. (Also, read this webcomic: http://comics.shipsinker.com/archive.php?arc=10doctors)

Here's an 8-bit Zelda medley.

Great to be Different by Forest Rain. 4-minute song that also inspired a fanfic. Warning to my fellow awkward people: you will cry during/after the video.

As EileenAlphabet mentioned, Peter Hollens and Lindsey Stirling do some excellent musical covers, Peter Hollens in particular seems to be working his way through some songs from LOTR.
Peter Hollens: https://www.youtube.com/watch?v=P24fsThGWSg&list=UUgITW70LNZFkNna7VsXbuQ, <a href="https://www.youtube.com/watch?v=8YnEMw3cRQ&list=UUgITW70LNZFkNna7VsXbuQ&index=3">https://www.youtube.com/watch?v=8YnEMw3cRQ&list=UUgITW70LNZFkNna7VsXbuQ&index=3, <a href="https://www.youtube.com/watch?v=pqD70Ivw7b0&list=UUgITW70LNZFkNna7VsXbuQ&index=4">https://www.youtube.com/watch?v=pqD70Ivw7b0&list=UUgITW70LNZFkNna7VsXbuQ&index=4, <a href="https://www.youtube.com/watch?v=dYxDKUGyNDg&index=34&list=UUgITW70LNZFkNna7VsXbuQ">https://www.youtube.com/watch?v=dYxDKUGyNDg&index=34&list=UUgITW70LNZFkNna7VsXbuQ
Alongside a very good song from Assassin's Creed 4: <a href="https://www.youtube.com/watch?v=3hMdoGet2A8&list=UUgITW70LNZFkNna7VsXbuQ">https://www.youtube.com/watch?v=3hMdoGet2A8&list=UUgITW70LNZFkNna7VsXbuQ
Alongside a number of medley's and other popular songs and themes (including Skyrim).

Lindsey Stirling links: <a href="https://www.youtube.com/watch?v=TCL94-MsxYc&list=UUyC4jvPzLiSkJkLIkA7B8g">https://www.youtube.com/watch?v=TCL94-MsxYc&list=UUyC4jvPzLiSkJkLIkA7B8g, <a href="https://www.youtube.com/watch?v=jLnL63cXmD8&list=UUyC4jvPzLiSkJkLIkA7B8g">https://www.youtube.com/watch?v=jLnL63cXmD8&list=UUyC4jvPzLiSkJkLIkA7B8g, <a href="https://www.youtube.com/watch?v=oNpmSAvpGQ&index=26&list=UUyC4jvPzLiSkJkLIkA7B8g">https://www.youtube.com/watch?v=oNpmSAvpGQ&index=26&list=UUyC_4jvPzLiSkJkLIkA7B8g, https://www.youtube.com/watch?v=BSLPH9d-jsI

The Piano Guys are the creators of the best version of "Let it Go" I've heard, by combining it in their normal style with Vivaldi's Winter. https://www.youtube.com/watch?v=6Dakd7EIgBE&list=UUmKurapML4BF9Bjtj4RbvXw They've also got some other very good bits of music including "Cello Wars" : https://www.youtube.com/watch?v=BgAlQuqzl8o&list=UUmKurapML4BF9Bjtj4RbvXw.

In a completely different vein of music to the other, I can;t go without mentioning Sabaton's awesome Shadows. When a metal band do a song specifically about Nazgul's it's gotta be good. https://www.youtube.com/watch?v=NlsRsRo1PI4

That's all for now
Storme Hawk

Fanmusic:
ShaDoWCa7 does wonderful covers. For the Tolkien fans there are her 'Misty Mountains' (all 27 verses) or 'Edge of Night'. She has also done songs from Dragon Age and Skyrim.
https://www.youtube.com/user/ShaDoWCa7

I'm also partial to artist like Lindsey Stirling and Peter Hollens, who will on occasion do covers of popular themes.
Here are The Rains of Castamere. https://www.youtube.com/watch?v=lvMhyO51Jv0
And a Zelda medley. https://www.youtube.com/watch?v=b3KUyPKbR7Q

Fanvideos:
I like good music/crack videos. A lot.
I can recommend jess9191 who does long but really funny videos. Here's one for Game of Thrones. (Warning, spoiler for third season.) https://www.youtube.com/watch?v=vZY5bxPuzbE She has also done Once Upon a Time and True Blood. Her serious stuff is also good.
Same recommendation goes to Katrin Depp. Here is her Doctor Who song-vid. https://www.youtube.com/watch?v=hYozkvT5ubU&index=4

Fanart:
There's these Tolkien fanart paintings, which I posted a couple of weeks ago, but which are good enough to post again: http://breathing2004.deviantart.com/gallery/30260599/art-of-Tolkien

There are some really good cosplayers in the Legacy of Kain section, but this was is mindblowing. http://sketchmcdraw.deviantart.com/art/Raziel-Soul-Reaver-Legacy-of-Kain-Cosplay-394485344

Oliver Boyd and the Remembralls, especially. I dare you to listen to Open at the Close and not cry. End of an Era, Flight of the Prince, Lupin's Tale, Just a Hufflepuff, Mischief Managed, and Train to Nowhere are my favorites.

My brother and I made a playlist (at our blog) that compiles a bunch of music videos that are truly A-W-E-S-O-M-E....

http://kittyandkay.wordpress.com/our-playlist/