I am developing an online banking site. Is it advisable to build a feature that allow user to download and save an image of their cleared checks on their computer? Is there any risk to user who download and save check image on their computer?
The chief risk in this is that the check has routing and account numbers on the image, so if someone were to intercept the download, they would have that information. Something like a MITM or hijacking your site to do XSS to download something besides the check image could be potentially harmful, but that's true of every site and not really specific to your question.
That being said, this risk of someone intercepting the download is relatively low and mitigated by using proper site encryption and secure downloading. SSL, HTTPS, proper certificates, that sort of thing.
The other, much smaller risk is if the end-users computer is compromised and the image is stolen from there - but this is well outside your liability and falls on the end-user to protect their data.