How can I move my spreadsheet files from MS Works 3.5 to Works 9?

Typically newer versions of software can read files from the older version. Best to back up the files first and keep a copy of Works 3.5 in case.

Looks as though I may be wrong: Technology Questions - View Single Post - How to read Works 4 .wps files in Vista [Works 9?]
You can try opening them on a computer that has Excel installed then save them as .xls.

If you still have access to the older computer, you can try putting a newer version of Works on it, loading and resaving your Works documents. I know Works 9.0 can read Works 6.0 or 7.0 docs, so that's the format you want to try to get them into.