I've seen quite a few people posting about Flash 8 apparently not supporting Flash Remoting and wanted to blog something about that. As far as I've seen the only issue is that the Flash Remoting installer hasn't been updated to install itself in the Flash 8 directory. If you're comfortable with working with the Flash Remoting AS2.0 classes the solution is easy, just download the Flash Remoting source code and then follow the instructions described here to copy the classes to the correct location on your hard drive (of course using the Flash 8 install directory rather than Flash MX 2004).
If you do need the FlashRemoting connector component and already have it installed with Flash MX 2004 what you can do is just copy the SWC over from the [Flash MX 2004]\en\First Run\Components\Data Components\ folder to [Flash 8]\en\Configuration\Components\Data\ then reboot Flash 8 and it will be listed in the components panel.
[update] You can get hold of the NetConnection Debugger and Service Browser panels by copying them from the [Flash MX 2004]\en\First Run\windowSWF\ folder to [Flash 8]\en\First Run\windowSWF\
[update 2] Macromedia now has the Flash 8 Remoting components and classes available for download. http://www.macromedia.com/go/flash_remoting_fl8