If you're going to move from MySQL 5.0.x to 5.1.x I would discourage such practice (it's been working fine for me when moving data between same versions of MySQL).
Use mysqldump (or phpMyAdmin export feature, or MySQL GUI tools backup feature) to export all your data to text SQL file. You can then load the file into new installation of MySQL (or use phpMyAdmin import feature, or MySQL GUI Tools restore feature)