Is there a way to check if a twitter username exists? Without being authenticated with OAuth or the twitter basic authentication?
As of right now, you're better off using the API the signup form uses to check username availability in realtime. Requests are of the format:
https://twitter.com/users/username_available?username=whatever
And give you a JSON response with a valid
key giving you a true if the username can be registered:
{"valid":false,"reason":"taken","msg":"Username has already been taken","desc":"That username has been taken. Please choose another."}
{"valid":true,"reason":"available","msg":"Available!","desc":"Available!"}
{"valid":false,"reason":"is_banned_word","msg":"Username is unavailable","desc":"The username \"root\" is unavailable. Sorry!"}
The reason this is better than checking for 404 responses is that sometimes words are reserved (like 'root' above), or a username is actually taken but for some reason the account is gone from the Twitter front end.