Are you SURE you want to store an array in one field of a database table?
I'd argue that in the vast majority of cases, the "right" way to do this is with several records in a related table. This will make the data easier to manage (you don't have to unparse and reparse the string) and much more flexible -- if you want to associate other data with the records, for instance.
Also: What if, in the future, you build a different front-end to this database? Data stored with PHP's serialize function is only accessible to PHP.
The serialize functions WILL do what you want them to, but having normal data structure is almost always worth the effort.
-foo