Gmail Desktop Gadget is a nice and free Windows gadget that will check your Gmail account automatically and let you know when you have new mail – even playing a sound optionally.
This Gmail Gadget occupies very little space and it is well designed.
Note that in May 2015 Gmail was unable to login to Google. You can download and try it by yourself, because some users reported it works again. In any case, if you have (or know of) some alternative Gmail gadget, please let me know to add it on this page. You can use also the Simple Google eMail Gadget, which, however, won’t notify you for new mail; it will only let you connect easily to your account and check by yourself.