Uploaded various modules - some are visible after the upload in the module admin area (as uninstalled modules) and some not. Any ideas that would help solving this problem?

Check that the modules have images and that you haven't unzipped them and left them in an extra folder, i do that accidentally loads..

Example: "What's new" module - no additional folders, version file present, image present, still no luck!? I checked the other modules as well - all seems ok? Any other suggestions?

some modules require additional files to be uploaded - CBB requires Frameworks and xoopseditor, Some smart modules need smartobject and so on - read the read me.

Try to enable phpdebug and look for errors when viewing module admin ...

Make sure your directory structure is correct. It should be:
XOOPS_ROOT/modules/modulename

Some modules come packaged from XOOPS_ROOT. Others from modules directory. A module directory has the xoops_version.php file in it.

File Permissions
Make sure that file permissions are set correctly for your server. I run into a number of modules whose permissions aren't set correctly for your server. The general aspect is 755 for directories and 644 for files, but your server may be different. Your ISP will be able to tell you what you need if these don't work.

That should be all of it. You can look at the directories of those that work and those that don't to try and compare based upon this info. Let us know if that solves it for you or not.