A helpful tip from Microsoft MVP Gail Shaw here on how to bypass a bad Logon Trigger:

Connections via the DAC don't fire login triggers. From management studio, open a new query and specift admin: before the server name (admin:MyServerName) and use windows authentication. You must be sysadmin.

If remote DAC hasn't been enabled (the default), you will have to do that from a querying tool on the server itself. If the server doesn't have management studio, you can use SQLCMD. Specify the -A switch

Once in, you can disable the trigger.

DISABLE TRIGGER MyBrokenLoginTrigger ON ALL SERVER

Be very, very careful when writing login triggers. If, for any reason, the trigger fires an error of Sev 16 or higher (object does not exist, database not found, permission denied) the trigger fails and rolls back the login.
I've had a couple panicked, late-night phone calls because of these.

Something that I have wanted to do for a while is to write a Logon Trigger for SQL Server.  This bit of code from BOL demonstrates how:

CREATE TRIGGER connection_limit_trigger
 ON ALL SERVER WITH EXECUTE AS 'login_test'
 FOR LOGON
AS
 BEGIN
  IF ORIGINAL_LOGIN()= 'login_test'
   AND (SELECT COUNT(*) FROM sys.dm_exec_sessions
	WHERE is_user_process = 1
	AND original_login_name = 'login_test') > 3
  ROLLBACK;
 END;

Next up: how to bypass a bad Logon Triger with the DAC (Dedicated Adminstrator Connection).