Todd (stuntdubl) has a great post at SEW on how to make a successful re-inclusion request to Google. He notes, first off, that a customer of his got banned specifically for using Link Vault, which is new information to me, as I had previously presumed that Google would not de-list sites for this but rather simply discount the value of the links.

Here's some of Todd's key rules:

• Fess up - If you did something wrong admit it and fix it
• Don't ASK WHY- You know what you did, or most likely some potential causes - At least fix those if you're going to ask WHY
• Don't whine - If it is the fate of your business you should probably be buying adwords anyhow
• Don't be a recidivist - pretty self explanatory - if you get special consideration and abuse it you won't get it again
• Don't bug 'em - G is NEVER probably going to get through their mountains of e-mail...don't make it worse
• Re-read the webmaster guidelines several times before sending off your request.
• Contact a professional and have them review your site for potential infractions, and diagnose if it is indeed a hand banning.
• Be polite

Todd's even got a good sample letter to send over to GG. I would actually consider hand writing, addressing and mailing this rather than using e-mail. Here's the address I'd opt for:

Google Search Engineering
Attn: Search Index Quality Control Team
1600 Amphitheatre Parkway
Mountain View, CA  94043