Shattr is a website where you can split your secrets into several shards such that if a certain number of them are combined, the secret can be recovered, but otherwise, no information about the secret can be obtained. (More information for crypto nerds can be found here.)
For example, you can Shattr your Bitlocker recovery key and distribute the shards to trusted third parties in several different countries. If you ever need your Bitlocker recovery key, you can use a secure ephemeral communications system (e.g. Red Phone) to obtain the shards and recover your Bitlocker key. However, it would be difficult even for a powerful adversary (such as a foreign government) to obtain enough shards to recover your key. You can also use Shattr to encrypt and decrypt files without the key ever leaving your browser.
All of this is done right in your browser, with no data ever being transmitted over the network. To prevent anyone from tampering with Shattr, always use HTTPS! For extra assurance, compare the hash of this HTML file with a known good copy (e.g. the one distributed on the DEFCON 22 CD). This file will never change.
For more information on how to use Shattr or how it works, check out these slides from the Shattr talk given at the DEFCON 22 Crypto and Privacy Village.
Shattr uses byte-wise Shamir secret sharing using Rinjdael's finite field (GF(28) with reducing polynomial x8 + x4 + x3 + x + 1). This means that partial shards can be used to recover a partial key. However, this also means we can support keys of arbitrary length, and using a small finite field makes the code much easier to write and audit (no big integer support needed!).
File encryption is done with 128-bit AES using GCM mode, which is an authenticated block cipher mode, so no MAC is required to ensure integrity. 128 bits should be adequate for most purposes, and is compatible with Microsoft's Bitlocker key encoding scheme, which is a bit more user-friendly than long hex strings.
If you are concerned about timing attacks or key material left in memory, you can run Shattr completely offline on a separate machine.