So, if I understand you correctly, you want to breed two different species and see what you get? "Hybrid" is the term to describe that. I think plants are the way you want to go, for time, difficulty, not to mention ethical reasons about working with animals (you are getting into mad scientist territory here). I suppose it might be possible to breed two closely related species of fruit flies or worms, but perhaps not that interesting to you--they'd still just look like fruit flies or worms and you might need careful analysis, or DNA work, to confirm the hybridization. There are indeed occasions where different animal species interbreed, for example horse+donkey=mule, but mules are sterile. (Ryan are you suggesting dogs and cats can be bred with EACH OTHER? that would be news to me) I think there are domestic/wildcat mixed breeds out there, too, for example.
Mixing two species is not necessarily an easy thing to do, because the definition of species is something that doesn't breed outside its group.
Here's a link I found with a summary of techniques to artificially breed plants:
http://www.ext.vt.edu/departments/envir ... 91pr4.html There are ways you can "help" the plants along to encourage them to breed with partners they normally wouldn't cross with.
And here's a whole book on the topic:
http://www.scipub.net/botany/fundamenta ... ction.html
Certainly flower growers are always trying to come up with interesting new hybrids like different-colored roses. You might try something similar, although there's no guarantee of success--probably the more closely related the two parents the better. Hybrids can be particularly weak or sensitive--or they can be strong, combining the best of both parents. I suggest Googling around for terms like hybrid, plant breeding, and see what you come up with.
Here's another thought--you could use artificial breeding techniques to determine the inheritance of certain plant traits such as flower color. In this way you'd be following in the footsteps of Gregor Mendel, the father of genetics, who controlled the breeding of pea plants to see what genes would be dominant or recessive. So for example you could cross two different-colored flowers, see what you get, and use that information to determine how the flower color is controlled.