700 Mhz and 800 Mhz eMacs maxed at Mac OS X 10.4.11 (link addresses how to upgrade).
No eMac is able to run off Mac OS 9 retail, and must use the prebundled copy of their eMac discs to install Mac OS 9 for use as bootable or Classic version of Mac OS 9. August 2002 and later models required the restore directions to install Mac OS 9 as either a bootable or Classic version.
1 Ghz and higher eMacs max at Mac OS X 10.5.8 (even with 10.5 there is no Boot Camp support on eMacs, and slower emulation was the only option to run Windows directly on an eMac). Only one eMac model M8950LL/A, was able to boot both into Mac OS 9, and use Mac OS X 10.5 via the Startup Disk System Preference in Mac OS X. The rest of the newer models must have a separate partition or external Firewire hard drive with 10.4.11 or earlier to maintain Classic compatibility, and could not boot Mac OS 9 directly. This limited their compatibility of Mac OS 9 drivers.
Booting Mac OS 9 on supported eMacs may only be possible after formatting with the Mac OS 9 drivers, which will require an erase of the hard drive.
That said, if you must run Mac OS X 10.6 or later, you'll need a newer Apple machine from 2006 or later with an Intel processor. This tip addresses how to migrate data from old eMacs or any Mac model that has a G3, G4, or G5 processor to an Intel processor: