I'm partial to using internal Lite-On drives  and putting them in external enclosures myself. Currently, the only burner I have is internal (I gave away a CD burner that was running externally when I put the internal DVD burner in).
External enclosure: BYTECC 5.25" USB 2.0 External Enclosure
There are plenty of other external enclosures out there. I've used different size BYTECC enclosures (or the same enclosure with other brand names) for a while now and not had any problems. I'm not terribly thrilled with the way they are assembled (they're a bit of a pain to put together and take apart) but I've never had any problems. They are available with USB 2.0, firewire, SATA, or combinations of the above. I have an external DVD drive (not burner) in a combination USB2.0/firewire enclosure that works well.
I got mine from E-bay it basically its a IDE to USB 2.0 convert that houses an internal IDE DVD burner.
I think this is the cheapest way to go. The IDE to USB 2.0 converter can be found for less than $30 each if you goto www.froogle.com and the drives are cheap now also. About $100 or so. I got mine as an all in one deal and it included a LG Burner. It came with good software but i have lost the software and canot find a replacement for it online.
I would not recomend getting an LG simply because their lacking in technical support. But i have not had any problems with it other than the fact that i cant find the software that come with it. I would check to see who offers the easiest and best customer and technical support.
Rupp, external as in for a PC or a set-top-box for using with TV? If it's a STB, I'd say holkd off for a while, they're as buggy as heck.
For PC-based, I like Squintz's recommendation. Just make sure your PC has good USB2.0. I recently had problems using an external USB2.0 HDD due to problems with the USB on my MoBo. A BIOS upgrade has sine fixed it, though.