Even if you have a Zip drive on your old Mac, you'd need to buy a second USB Zip drive for the iMac to use the discs, thanks to the iMac's lack of SCSI. The solution? Network the two machines and transfer your files that way. This is a lot quicker than moving them across on Zips, it's actually cheaper than a Zip drive, and at the end you'll have two networked Macs for playing multi-player games and the like.
Before you start, you need to know whether your old Mac is Ethernet-ready. Most Power Macintoshes have built-in Ethernet, and some high-end older models are also equipped with Ethernet cards. Your iMac has such a port, and ideally your old Mac should have one exactly like it.
Techie bit: the Ethernet port on your iMac conforms to a standard called "RJ-45". Some older Macs use a variant of the Ethernet standard called "AAUI". If you have one of these you'll need an AAUI to RJ-45 converter. These are fairly easy to find, and not expensive.
Once you've ensured that both of your Macs are Ethernet-ready, you need a bit of wire to connect them. Start out by buying a "cross-over" cable. Cross-over cables are different to ordinary Ethernet cables in that the send and receive wires are switched, so that the send wire on one end corresponds to the receive wire on the other. Not all Ethernet configurations will work with a cross-over cable, but since they only cost about $15 it's worth investigating. If you're connecting two iMacs, or an iMac and a G3, a cross-over cable will work. If you follow these instructions and find that a cross-over cable doesn't work, invest in a hub. A 10/100Mbps Ethernet hub will cost you less than $150 and provide all the speed you need. (It's also cheaper than a second Zip drive.)OK, so now the two machines should be connected, either with a cross-over cable or with two bits of cable and a hub. The next thing is to make sure both computers are communicating via the Ethernet you've just set up. Open the AppleTalk control panel (or the Network control panel on an older Mac) and select connection via Ethernet. On older Macs, click on the EtherTalk icon. When you close the control panel, you should receive a dialogue box asking if you want to activate AppleTalk. Click OK. If you don't get this dialogue box, open the Chooser and activate AppleTalk manually.
Then, choose which machine you want to use as a server. This should be the older and slower of the two machines. Open the File Sharing control panel (or Sharing Setup on some older Macs). Fill in your name, a password and the name you want to call your old Mac on the network.
Then, on the new machine, open the Chooser, then click on the AppleShare icon. The name of your old machine should appear in the window on the right. Double-click on it, then fill in the owner name and password you selected before. A dialogue box will appear with the names of all volumes (hard drives, Zip drives, CD-ROMs, etc.) mounted on your old machine. Select the one you want and click OK.
IMPORTANT NOTE: Whatever you do, don't check the box next to the volume name in the dialogue box. This will force your machine to try to log on to your old machine every time it starts up. Trust me, you do not want this.
Your old hard drive should now be visible on the desktop of your new machine. As a bonus, you now have a nice speedy network for multi-player games. But that's another how-to.