Applying MySQL 5.1 bin log to MySQL 5.5 Is it possible to apply MySQL 5.1 bin log to MySQL 5.5. 

I am assuming that bin log is portable between two machines (same OS, Architechture but different machines running same version of MySQL)
It is possible to replicate from an older version 'master' to a new version master for the next higher major version (5.1 to 5.5 for example): http://dev.mysql.com/doc/refman/5.5/en/replication-compatibility.html

Of course bin logs are portable to the same architecture running on different machines, or replication would be almost useless (there are difficulties with running on different OSes, though).

Since your question only asked about applying a bin log to the second server, I might mention that if you don't have the 'master position' of when the second server should begin reading the binary log, you might have inconsistencies in data. Especially if it has been a long time since you've taken a full backup and no longer have the relevant log entries.

But at the heart of it, Binary Logs from an older major version to the next major version is supported.