The "Mule" orchid?
 

Which plants can you hybridize with each other and how far can you push the limits. Is there a point a which crossing a "horse" and a "donkey" produce a sterile "mule". It was just something I was thinking about when I was watching the Humanzee special on the Discovery Channel.

in general, you can cross any 2 plants of the same alliance. if you cross 2 plants with a different number or size of chromosomes, it's likely to produce a sterile hybrid

and keep in mind that hybridization in plants behave a bit different than in animals ;) while in animals, it is the rule to have sterile offspring, in plants it is quite common to have fertile offspring (if you manage to get get offspring at all!)

As Lambelkip said, the trick is crossing within the same tribe or alliance. However, this does not always work: e.g. Cattleya x Epidendrum works in most cases; Phragmipedium x Mexipedium, does not work at all (or at least it has not worked yet!)

Crosses within an alliance generally work and the offspring are viable. There are crosses between tribal sections that work (Catasetum X Cymbidium, etc.) Whether the offspring are fertile or not is something I haven't researched. Yet.
Due to certain allelial positions, some as close as species in a genera will not cross. this is especially true in genera such as Dendrobium.
This is one basis for creating new genera.

Do you think you could cross a terrestrial lady slipper with a non-terrestrial one.

if you check this link, you can see most of the primary hybrids that have been done in the genus Paphiopedilum:

Paphiopedilum Primary Hybrids


and in this one, in the genus Phragmipedium:

Phragmipedium Primary Hybrid Photos

maybe this answers you question regarding ladyslippers...

Very cool thank you for the website very informative.

Ramon,
Really great reference sites!! I don't know if there is written material to go with the site, but a fair number of the Phrag crosses they show using besseae are obvious offspring of Phrag besseae var. flavum. Could not both that variety as well as var. coloratum be shown?
I'm not sure if I want to look at the Phrag site again. It makes me want to go out and purchase some more Phrags!!!!

Great sites, thanks Ramon.I have a Krull-Smith cross of Paph. stonei x Paph. kolopakingii that I did not see on that list....maybe I should send them a pic.