Is there a way to have iOS remember passwords to HTTP authenticated sites?
It seems that Safari on iOS doesn't support this natively. You have a couple options:

Workaround:

If you're not too worried about security, you can embed the username and password in the link itself, and bookmark that:

http://username:password@hostname.com/...


(Also of note: it sounds like iOS may pop up a warning when you visit a link that includes a username and password.)

Alternative:

There is another browser called Atomic Web Browser [App Store link] that can autofill HTTP authentication, among many other neat features.