How many External Hard Drives can I plug to Airport Extreme?

The constraint is be the number of ports available on your USB hub.

Any connected hard drives should appear in Mac OS X. Use a self-powered usb hub and connect hard drives your hub. Only then will multiple external drives have enough power to run.

Also see store.apple.com for related questions.

As shown on the Apple website, the Airport Extreme has only one USB port:

However, you can use a USB hub to connect multiple devices to it.

(I also wouldn't be surprised if Apple eventually creates a Thunderbolt-compatible version of the Airport Extreme — and Thunderbolt devices can be daisy-chained, so you might be able to connect more than one hard drive at a time.)

For a single hard drive, you might also like the Time Capsule which has an integrated hard drive.

For a more flexible and heavy-duty solution for multiple drives, you could use something like Drobo.