Forge's SHA-256 implementation is fast and reliable.
To run tests on several SHA-256 JavaScript implementations, go to http://brillout.github.io/test-javascript-hash-implementations/.
The results on my machine suggests forge to be the fastest implementation and also considerably faster than the Stanford Javascript Crypto Library (sjcl) mentioned in the accepted answer.
Forge is 256 KB big, but extracting the SHA-256 related code reduces the size to 4.5 KB, see https://github.com/brillout/forge-sha256