The browser has to download files before it can display them, even if it only to the cache or a temporary location. Saving files gives your antivirus software time to check the file before you open it, so other than the extra step of manually opening the file there's little real difference. (And you can double-click the "Download completed" message to open it, you don't need to go searching through your folders to find it.)
No, Opera doesn't allow you to open files directly - but it isn't really that hard.