Q: How do I backup from my iMac CRT to an external hard drive or transfer data to another computer?

Which model iMac do you have - one with a tray-loading or a slot-loading optical drive?  I'm assuming that you don't have the slot-loading model with a CD-RW drive.  From a standpoint of transferring directly to an external backup medium, you have the choice of a USB-connected flash drive, hard drive, or optical disk-burning drive for any model G3 (CRT) iMac.  The slow USB 1.0/1.1 bus limits data transfer speeds to a flash drive or hard drive, and limits CD burning speed to 4x.  With the exception of one slot-loading model, the remaining slot-loading iMacs have onboard FireWire 400, which provides a much faster bus than the USB 1.0/1.1 bus.  In terms of potential maximum speed, the difference is 400 megabits/sec for FireWire, compared to 12 megabits/sec for USB 1.0/1.1.  I've used USB flash drives with my iMac DV 400s and they were more than adequate for backup purposes.  When plugged into a newer iMac with onboard USB 2.0, you'll see the faster speed when downloading files from the drive.  With prices for USB flash drives dropping everyday, you can get a sale-priced 16 GB drive for about $15 now.  If you need more storage capacity, you could opt for an external hard drive.  Keep in mind that the small, external USB hard drives don't require a separate power supply, because they're bus-powered and draw the necessary 5 volts from the USB port.  They must be connected to the iMac's unused port on the side of the computer and not to the keyboard or an unpowered USB hub.  A powered USB hub connected to that second USB port would also work.  An external FireWire-connected hard drive will likely be a standard 3.5" drive installed in an enclosure that uses a separate power supply.  If you know which newer model iMac (and OS version it's running) that you'd be transferring the files to, you could consider networking the two computers.  I prefer the convenience and flexibility of having files stored on an external medium.