How many characters in varchar(max)?

From http://msdn.microsoft.com/en-us/library/ms176089.aspx

varchar [ ( n | max ) ] Variable-length, non-Unicode character data. n can be a value from 1 through 8,000. max indicates that the maximum storage size is 2^31-1 bytes. The storage size is the actual length of data entered + 2 bytes. The data entered can be 0 characters in length. The ISO synonyms for varchar are char varying or character varying.

1 character = 1 byte. And don't forget 2 bytes for the termination. So, 2^31-3 characters.

For future readers who need this answer quickly:

2^31-1 = 2 147 483 647 characters, or roughly 2.147 billion

See the MSDN reference table for maximum numbers/sizes.

Bytes per varchar(max), varbinary(max), xml, text, or image column: 2^31-1

There's a two-byte overhead for the column, so the actual data is 2^31-3 max bytes in length. Assuming you're using a single-byte character encoding, that's 2^31-3 characters total. (If you're using a character encoding that uses more than one byte per character, divide by the total number of bytes per character. If you're using a variable-length character encoding, all bets are off.)