Luckily, the ASU library system provides an off-campus scholarly portal from my.asu.edu (under the "Library" option on the left) that can be used to make your off-campus connection look like an on-campus one so research databases will grant you ASU-caliber access. Unfortunately, if you've clicked on a link to a paper, you have to re-do your search within their portal to get your off-campus access, and that's really inconvenient. So I've come up with a shortcut (similar to my OSU LOCSI shortcut).
Drag the following bookmarklets to your "bookmarks toolbar" (that strip of bookmarks that rides just below the "location bar" in your browser).
- ASU LOCSI ("LOCSI" = "Library Off-Campus Sign-In")
(feel free to rename that bookmarklet as you wish; the name "ASU LOCSI" isn't important to their function)
I hope that helps.