I plan to take out the hard drive in a Maxtor OneTouch 4 external drive and replace it with a bigger hard one. The original hard drive is 750GB. Will it still work if I put in a 2TB hard drive?
It should theoretically still work. The only components inside of many external cases are a eSATA and USB bridge that provides power and USB ports to plug your cables into. Other than that there's very rarely any logic going on inside the external housing that would limit your drive size as long as it uses the proper interface connection (IDE vs. eSATA) and the proper power adaptor (4-pin DC vs. eSATA power).
Yes, it should, with one caveats:
Namele, Some manufacturers external caddies will only work with that manufacturer's drives (I have a WD Mybook, and it will not show up unless the drive is also WD).
That said, The chances of your external caddy working with a different sized maxtor drive are very high. As for any other brand drive, I would recommend testing it with a drive you have on hand before doling out the cash for a big drive.
Edit: I've only seen this for USB and Fireire. I don't know if it's true if you're using e-SATA.