Mantis does show images inline, as long as they're below a certain size (which is configurable). The image in 0008798 is shown inline.

I think there was talk of an attachment display plugin mechanism which might allow other filetypes to be displayed. Displaying .doc or .xsl files seems like a very very large undertaking however so I wouldn't keep my hopes up for that.

Cool! I just found this out!

However, I think the answer doesn't quite fit the question. The question I think is:

"If I click on an attachment, and the attachment is of a type that the browser can display, e.g. image, then display it in the browser instead of showing me a download dialog"

This has to do with the following header:
content-disposition: attachment; filename="Contoring+current+result.jpg"
which forces a download dialog box.

Can we make this optional behaviour?

Edit: ticket 12313 answered it for me.