[Travis_Flesher]

If humans could make dogs immortal, should we?

Absolutely they should! Genetic engineering is one of the coolest things earthlings can accomplish. A philosopher's stone like that is a different ballgame than traditional selective breeding for desired traits, but with an open mind and some magical thinking, I believe it's possible. The immortality would probably utilize cybernetics and biotechnology.
It's interesting to note that natural selection has not favored deformities, but if a reasoning mind uses unnatural selection, we could be breeding animals or even, egad, humans, with 6 arms, 4 legs, 2 heads and other possibilities. In the distant future there could be people with perfectly formed additional limbs like Giro from Mortal Kombat.