I\'ve create a maintenance plan on my SQL Server 2005 server. The backup should be written to another server. I\'m using a UNC path for this. The user running the SQL Agent jobs
Check the he account SqlAgent is runs on. Usually it system\NetworkService ant it does not have access rights on other computers.
Either give temporarily write rights to everyone on the UNC path or in Control Panel/Services change the account used for SqlAgent.