Well I wasn't really sure what to call this, but basically I thought it would be useful to gather a list of sites/forums that specialise in romhacking (Although it's mostly forums at this stage).
The main reason for this is that there have been occasions where I thought I had discovered something new, only to have a random search and find a topic buried away in a forum about the very same thing!

Please feel free to add to this list as I'm sure that there are many more!

General Romhacking

Jul
DataCrystal - Wiki for Rom Data
Sonic Retro Forums Technical Discussion (Has random general romhacking related info; not just Sonic)
Rusted Magic - Rom Hacker Central
Zophar.net - Rom Hacking
X-Cult - Haus of Hacking
SMW Central - Rom Hacking

General Romhacking - Archived

Acmlm's Board - I3 Archive
Acmlm's Board - Rom Hacking Archive (Older Archive)
Rusted Magic - Rom Hacking Data Repository

Gameshark/PAR Codes (Good for memory addresses)

Gameshark Central
The Ghsi (Be sure to check out the forums as well as the main site)

Game/System Specific

Final Fantasy 4-6 - Mnrogar's Den
Final Fantasy 4-6 - Slick Productions
Super Mario 64 - Jul - SM64 Hacking
Rare (Goldeneye, Banjo-Kazooie etc) - RareWitchProject (Now an archived forum?)
Donkey Kong Country - DKC Atlas
Golden Sun - Golden Sun Hacking Community
Advance Wars - Wars World News Forums
Pokemon - Pokecommunity Forums
F-Zero - MrFixitOnline
Fire Emblem - Fire Emblem Planet - Coding, Hacking and Programming
Fire Emblem - Serenes Forest
Gbatemp - DS and GBA Hacking
Puyo Puyo Series - Game Rips and Modifications
Super Mario World - SMW Central
Megaman Series - Interordi.com
Earthbound - Starmen.net - PKHack Forum (Mostly Earthbound, but some other games spread about)
DS Rom Hacking - DS-Scene.net

Game Development

Sega Genesis/Megadrive/32X/MegaCD - Sprites Mind
NES - NesDev Parodius

Most of us GE/PD hackers frequent this place. There's also the Vault and Wiki with additional information.

Here's my website I created for FF6 hackers. It's main goal is to offer sprites to the rom hacker.
FF6 Resources

I have 32 custom sets of FF6 player sprites available. All of which are titled, credited with the authors name (if the authors name is available) and given a accurate description. Members can also rate these submissions. This site is different than your typical sprite website because it:
A: Is directed towards the FF6 hacking community.
B: The sprites are set up into a working sprite sheet which is formatted for the use of FF3SE.