Which version of MySQL should I use?
You need to get away from MySQL 5.1 ASAP

MySQL 5.0 Active Support ended on December 31, 2009 - Now in Extended Support Phase
Per the MySQL Support Lifecycle policy, active support for MySQL 5.0 ended on December 31, 2009. MySQL 5.0 is now in the Extended support phase.

Versions have changed rapidly since Oracle stepped in


MySQL 5.1.61 released 2012-01-11
MySQL 5.1.60 released 2011-11-18
MySQL 5.1.59 released 2011-09-16
MySQL 5.1.58 released 2011-07-05
MySQL 5.1.37 released 2009-08-02 ( pretty aged by now )


MySQL 5.1 will soon reach its EOL (End of Life) in terms of Active support and go to Extended support (EOL : TBD). Naturally, that support is commerical. It would not hold my breath for that kind of support for the Community versions.

MySQL 5.5.20 was just released 2012-01-11 and 5.5.19 was just a month ago. As with any upgraded product, always read release notes to see what changes and improvements have come about since the previous stable release.