I use google apps, which is probably the same spam filter as gmail, spam just gets filtered to a 'spam' folder, which it is automatically deleted after 30 days if you leave it there.
Its pretty good, but sometimes a bit overzealous, on one occasions it classified as spam one of google's own domain management confirmations, an email that was auto-generated by google.
My main domain gets around 50-100 spams on an average day, much more during 'storms'. But most are addressed to what look like random names, like "hgfdd8475@*****.com". And of course, I get the non-delivery reports for spam spoofed from my domain, but again that tends to use made-up names. So careful setup of the 'catch-all' user makes things manageable.
Properly addressed spam matching a valid user name is only about 2 or 3 a week, despite the fact that one of my addresses ("support@******.com") is free visible for all to see on a crawlable web page.