Use " instead of " to escape it.
web.config is an XML file so you should use XML escaping.
connectionString="Server=dbsrv;User ID=myDbUser;Password=somepass"word"
See this forum thread.
Update:
" should work, but as it doesn't, have you tried some of the other string escape sequences for .NET? \" and ""?
Update 2:
Try single quotes for the connectionString:
connectionString='Server=dbsrv;User ID=myDbUser;Password=somepass"word'
Or:
connectionString='Server=dbsrv;User ID=myDbUser;Password=somepass"word'
Update 3:
From MSDN (SqlConnection.ConnectionString Property):
To include values that contain a semicolon, single-quote character, or double-quote character, the value must be enclosed in double quotation marks. If the value contains both a semicolon and a double-quote character, the value can be enclosed in single quotation marks.
So:
connectionString="Server=dbsrv;User ID=myDbUser;Password='somepass"word'"
The issue is not with web.config, but the format of the connection string. In a connection string, if you have a " in a value (of the key-value pair), you need to enclose the value in '. So, while Password=somepass"word does not work, Password='somepass"word' does.