It will not make you bulk up. Look at Olympic sprinters; they are athletic yes, but by no means towers of flesh, certainly don't have a "rugby player" physique. I don't know what exactly the OP wants, but if it's being big then sprinting won't achieve it, regardless of how much you eat. It doesn't work your arms, shoulders, back etc. nearly as much as weightlifting supplemented with lots of protein. And FYI your arms aren't the only thing you can train with weights so you certainly won't be a "weak puny guy with big muscular arms" (which is a bit of an oxymoron as arm muscles are some of the most often used in the body).

OP: When it comes to physique, useful is best. And IMO when the usefulness of physique is concerned fighting is the most important. I guess "optimal" for a fighter would be a somewhat-bulky build; something like http://images.starpulse.com/Photos/Previews/Bronson-movie-m06.jpg or http://www.therichest.com/wp-content/uploads/Mike-Tyson.jpg. Not "ideal" fitness according to society but a bit of extra padding over muscles helps absorb hits. Of course if you actually want to use it for anything you'll have to learn to fight too.

The best fighter in the world is tall and skinny, incidentally he is built almost identically to the fastest sprinter in the world. They're both 6'4" lanky and wirey endomorphs of west african descent.

Talking of course about Jon Bones Jones and Usain Bolt.

Ofcourse no amount of any type of exercise will give you their genes, but I believe sprinting intervals are the most complete workout to make your body as good as it can be.

Push Ups/ Pull ups

Weights if you want to be extremely fit

Best fighter; might as well have said "best band" or "best painting" etc. But let's entertain this idea; the fact that they "look the same" means nothing. You can take someone with a sprinter physique; someone who looks exactly like Jon Bones Jones and put them in a ring, to have them knocked out in two punches by a guy who looks way less fit but is simply tougher/more experienced/more skilled etc. Furthermore, there is no such thing as an "ultimate" physique, just one best suited for a particular purpose (ie. fighting, which I emphasized in my post). If you realized that perhaps you wouldn't defend such a hopeless argument.

EDIT: I was kind of all over the place there so let me recap. When I said a certain bodytype is highly suited for (if not ideal) for most fighting sports, you contradicted me by providing a freak example of someone with a great amount of talent, and possessing the bodytpe you mentioned. Essentially this does not disprove my argument as it brings another factor into play; namely Jon Bones Jones' fighting ability. If it were hypothetically possible to reproduce that exact ability into a fighter with the physique I mentioned (so they would be equally matched in every respect except physique) then that fighter would have the advantage by strength. And yeah that does seem very obvious but it's what I was trying to tell the OP with my original post.