I recently upgraded from windows Vista to Windows 7 ultimate. My printer spooler service is set to automatic but keeps stopping. As a result I can't install my printer or use network printers to print publicly. Is this a usual problem for computers from vista to 7?

Any upgrade process is fraught with problems and considering you went from Vista (pants) to Win7 (way better) I'm not really surprised you are seeing issues.

If you are lucky you can use your upgrade disc to do a repair install of Win7.
This is quite straightforward and detailed here: Repair Install - Windows 7 Forums

This should "reset" things so it will work.
Also make sure you have applied ALL available updates and patchs as there has been quite a few already.

Here is a few more links related to print spooler here.

Ref:

The print spooler will not stay on in Win 7.

Print Spooler | Services Guide | Smallvoid.com