IMHO, I think this is one of those things/topics that should NOT have a "blanket answer" - but rather, this is should an individual thing per campaign.
Why? As several posters already pointed out it _can_ add to myth and creation stories. At the same time, however, it can also change the tone (no telling where the players' minds will go once you start talking about breeding with animals and what not - regardless of the breeder's physical form).
I think it's safe to say that this is one of those campaign decisions that do not need to be detailed unless/until it actually comes up
Bottom Line: This decision has the potential to add to the game but also has the potential to detract from it. Most people haven't even thought about or considered it. For those that have, it should be left as a campaign-specific decision/implementation.
Now, having said all that, I can only presume the original poster is at the point where he is giving it thought and consideration and is thinking about implementing it for his campaign. No argument given should be a blanket-statement to cover all campaigns so we are really talking about his campaign and his campiagn alone.
So ...
a) You are talking about two separate issues here (from what I can see in my cursory glances) - wildshaped druids breeding with animals and awakened animals breeding
b) does allowing either of these breedings add to your campaign? ie could they add to your creation myth (or do you already have creation myth solidifed), could they add plot lines that you want to use ?
c) do you know your players well enough that this won't be taken into some immature tangent once you start explaining/revealing that the creature they face is the love child of their druid ally and his pet dog?
d) is the druid mythos leinient enough to not view breeding in this manner wrong?
e) (insert something witty and smart here -- I'm just too tired right now to think of something though, almost 5am..

)
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From a real-world biological standpoint, wildshaped druids and animals would not produce offspring because the druid (aside from appearance and ability) is still a humanoid and the animal still an animal (or magical beast or whatever). Awakened animals could interbreed IF they are of the same genus (or some other level of biological classification that I don't recall). If they are not then they can not produce ofspring. If they are of the exact same species their offspring could reproduce into further offspring thus continuing the chain.
I'm reminded of the horse and the mule. They can reproduce together because they are of the same genus. But because they are not the same species, their jack-ass offspring are sterile. (it's late and I may be giving things the wrong name but that's the basic idea).
But campaigns are not the real-world, I am merely including this for comparison.
Now that I am thourghly disguested by the thought of someone LOVING thier pet (as someone so elequantly put it earlier) I am going to read myself to sleep and hopefully put the mental image out of my head.
