Why do most fighter craft have a center stick?
At present, it appears to be a design choice rather than any other thing.

Most of the present generation fighters are transitioning to side-mounted sticks from center sticks. Almost all of the US combat aircraft have side-sticks. In Europe, it's somewhat of a mix- Typhoon (and Gripen) have center sticks, while Rafale has a side stick. The Russians are sticking to a center stick in the T-50.

The location of the control stick depends on a number of factors:


Ergonomics- Side stick is better in this regard, limiting the display area in the center; this might be a problem in smaller cockpits.
One of the reasons for using side stick in F-16 was that it (the hand-rest) supported the Pilot's hand during high 'g' maneuvers, along with the inclined seat (which is also being used in a number of aircraft).
There is also the personal choice- some pilots may prefer using a center stick, and others, the other way around (there seems to be little problem in transitioning from one to another).


Historically, combat aircraft have had center sticks. Side sticks have come about after fly-by-wire controls. Eurofighter has the following to say in this regard:


  Every military aircraft cockpit design has to be something of a compromise, but in a small cockpit, a center stick can cause particular ergonomic difficulties, perhaps limiting the size of the display area for the instruments and/or screens ... That is when options are considered, and one of those would be the sidestick as used in the F-16. However, if the cockpit is sufficiently large and the geometry of the seating position is correct, there is no reason to have anything other than a center stick—and the pilots of the four partner nations agreed. The choice between center sticks and sidesticks is 40% personal—the balance being on technical grounds. We find that F-16 pilots convert easily and naturally to a center stick.