I think you will find that most, if not all fighter aircraft have centring stick (whether modern or otherwise). It is just the mechanism of centring which is will differ with age.
Older aircraft will have fully reversible controls, which basically means that the stick is physically connected to the control surfaces (whether mechanically or hydraulically, or combination of both). When the aircraft is moving through the air, the flow over the control surfaces make then tend to return to their equilibrium point, thus centring the stick. The actual equilibrium point can be modified by deflecting trim tabs on the control surface, which will move the centring point of the stick (thus keeping the aircraft in "trim"). The amount of force pushing the stick to the centre will increase as the stick is moved further away from the middle due to more aerodynamic force being exerted on the control surface. Additionally things like "bob weights" are sometimes added to further increase the force to stop pilots over-stressing the airframe - such as in the Hawk and the Hercules (all right, not a fighter but an example none the less)
When on the ground, there is no airflow, so the stick will likely fall to the position based upon the weight of the control surfaces themselves (i.e. the stick will fall forwards under the weight of the elevator drooping towards the ground).
Modern fighter aircraft, such as Typhoon, will have High Order Flight Control Systems (Fly by Wire). With these the stick has no physical connection to the control surface and essentially has some very high quality potentiometers (resolvers) at the bottom of the stick to sense the stick position. These sticks will be centred using springs, but could also use additional devices (commanded by the Flight Control System or otherwise) to change the stiffness of the centring spring to provide better feedback of the aircraft parameters to the pilot. The electrical signals from the stick feed into the Flight Control System and the computer works out where to put the control surfaces to provide the desired aircraft flight path.
The Flight Control System will no-doubt have some clever algorithms to provide Care-Free handling (or put another way "Care-Less handling"), so that the pilot in theory will not exceed the aircraft structural limits. The Flight Control System may (very likely) also change the parameters that the pilot is controlling to. For example, pulling back on the stick may provide a "g command" or an "alpha command" or a "pitch-rate command" depending upon the where the aircraft is in the flight envelope and what the role of the aircraft is.
The main type of aircraft where the stick does not centre is going to be something designed with aerobatics and very high manoeuvrability in mind, like a Yak 52 or and Extra (Redbull air race type aircraft). Although fighter aircraft are highly manoeuvrable, they must also be easy to fly. This allows the pilot to be looking over his shoulder for the enemy aircraft, looking at his ground target, or playing with the RADAR. Therefore in important role of the stick is to "talk" to the pilot, so he knows what the aircraft is doing without looking through the HUD or at his flight instruments.
Does that help?