Thought I would post how I was able to upgrade from F15 to F16 without the use of "preupgrade", and some of the obstacles I ran across that I was able to resolve fairly easily. This may not be the best way to do this, but it worked for me, and I'm happy with the results. In a month or so, I plan on doing the same thing again to upgrade to F17...
1.) The first step is to back up all your important data, configuration files, etc... (in other words, the whole system!)
2.) As root, make a new folder called "repoback" and copy all files from /etc/yum.repo.d folder to this new folder (it can be placed anywhere, I placed mine in / )
3.) Modify each of the repo files in the /etc/yum.repo.d folder, one at a time, and change any instance of "$releasever" with the version number you want to upgrade to. I entered "16" since I was currently running 15.)
4.) Within each of these files are different sections, and in each section you will have to replace the "$releasever" with "16" twice (if I remember correctly).
5.) You will also have to edit each line (2 or 3 per file) stating "gpgcheck=1" and replace it with "gpgcheck=0", unless you have imported the GPG Keys for the newer OS version.
6.) After editing each of the files, you will need to update RPM and YUM, using the commands "yum update rpm" and "yum update yum" (in this order).
7.) Once this is complete, run "yum update", and allow it to upgrade your OS.
8.) After this is complete, reboot your system and run another "yum update".
9.) Now, copy back your original repo files on top of (overwrite!) the modified ones from before.
Now, this is where I started having some minor issues. After the reboot, and during the second "yum update", it wouldn't update one application. It happened to be a "chess" game, so it was no big deal, I just did a "yum remove chess", and then the "yum update" and all was fine.
Also, I probably should have rebooted a second time after this, however I did not, and I am seeing some instances of mounted shares not mounting properly, SQL database connection errors, Web service errors, and a couple others. I fixed each of these as they happen, by simply restarting the "offending" service - ie. service httpd restart, or service mysqld restart.
Other than these two minor issues, everything is running smoothly!