What animals stop other members of their species from mating and why?
As the comments suggest, I think a little basic reading so you understand the definitions involved here might be appropriate.  The questions are a bit anthocentric, and I think that's why folks with a bit more biological culture might be concerned about the answers.  

Alpha type structures can be found in all sorts of animals.  Sperm competition, where many males simply mate with the female and let the sperm work it out are also v common from snakes to mice to primates.  

Its hard to say without you asking a more specific question, but the essential question is whether the competition occurs between the animals themselves or between the intermixed sperm of the males inside the female.  If that sounds gross, that's a typical reaction if you are not a monkey, snake, duck or mouse to name a few.  Different species choose different social roles in mating and for reasons that may be difficult to divine. 

For animals in an alpha troop modality, the alpha male will eventually get older or weaker and the younger ones will have their chance to mate.  There is always tomorrow.  That's my very brief answer.  

It might be worthwhile to take some time to read some about this - a page of response to your questions is not going to really answer your questions.  (I say this having answered several of them :).  I would recommend "The woman that never evolved" by Sarah Hrdy.  As a feminist in the 70s Hrdy decided to do a survey of primate male/female roles in mating, to try understand how human men and women became who they are (and who has not wondered this?).  This book will give you an idea of how so many different animals have come to different roles and possibly why.  

Since I have a little time today, I'm adding a couple of tangential references:  Mice sperm have responded to sperm competition so much by evolving hooks on their heads and chain up together and swim together which enhances the chances of paternity.  Ducks are quite different.  they have a lot of forced copulation, but female choice of mate is still quite influential.  Duck vaginas are very complicated, with corkscrews and dead ends to make it difficult to copulate without 'consent'.