Jade Cocoon 2(PS2) had some pretty good breeding mechanics. It plays very similar to pokemon, but breeding was the lifeblood of your team, splicing and hatching higher tiers of evolution in order to breed ever fearsome babies. I certainly have fond memories of the game.
There's also Creatures 2, which was a game with no end goal, just to explore a pretty lovingly crafted 2D world. You'd raise your original Norns (a monkey/furby cross breed) baby to adolecence and teach them like you would a pet, then lure them off to explore, discovering lost technology and other nifty stuff. It was pretty damn immersive and impressive to 6 year old me. Breeding was integral to keeping up the gene pool and dealing with death was a big part of the game. Just make sure you patch it, because otherwise your Norns suffered from One Hour Stupidity Syndrone, where they'd forget to breath and eat after and hour of growing up.
It can also get pretty fucking dark, they had a geneticist on hand to guide them in making it as realistic as possible. So it's entirely possible that your creatures can be born with real life issues such as crippling brain defects (no that's not a jab at the games AI), lung problems causing them to be wracked with pain, paralysis of the limbs etc. You can still look after them, or put them down. As a childs game, it certainly forced them to confront concepts of life they may not be quite ready for. Genetic defects can be inhereted, skip generations, the whole shebang.
The whole game was pretty damn complex, giving you every detail of your creatures right down to a nanoscopic level. The game was really innovative (as far as I'm aware) in not only level of complexity of AI and build of the creatures but also of giving you a really fleshed out world, but forcing you to discover it from the creatures point of view. It's sort of like Dark Souls in that respect, you don't know much and there's no one here now, but the atmosphere definitely tells you that there was something here before. It's empty and yet...full at the same time.