How to convert mysql database charset to utf-8
http://dev.mysql.com/doc/refman/5.1/en/alter-table.html


  If you want to change the table default character set and all
  character columns (CHAR, VARCHAR, TEXT) to a new character set, use a
  statement like this:
  
  ALTER TABLE tbl_name CONVERT TO CHARACTER SET charset_name;


Follow the link for more details.  

Be sure to do this in a test enviornment first.  You probably wont run into many issues going from latin1 => utf8 but in general you might run into collation "weirdness" when converting charsets.  This is especially true if you have any kind of unique constraints on char-ish columns. 

Also keep in mind if you do have any char or varchar columns indexed moving to utf-8 will triple the amount of memory needed