For bank statements, your bank (probably) should have them available online. I know both WaMu and Wells Fargo provide online versions of statements going back to the creation of the account (up to 7 years). They're just PDFs of the version you get in the mail so I look at the statements as they come in and then toss them.

I like the electronic approach, but depending on your comfort level with your bank, you might want to keep a copy of that PDF in your own file.

B of A does it too, but I am not sure how far they go.

Probably seven years. Banks are legally required to keep them available for that duration so I imagine most of them figure if they have them, they might as well make them available because sending out paper reproductions is expensive.

One caveat, this isn't to say that all 7 years are immediately available, as that would be pretty expensive from an infrastructure perspective. There will probably be a point at which they have to be retrieved and then cached for online presentment. At WaMu this takes about 24 hours and happens for statements older than 18 months.

B of A keeps them available online for 2 years.