With the larger aircraft unless it is tight the nose wheel steering is anough for turning.
Where large aircraft need to turn on the runway to backtrack for a turn off yes the engine power does need to be used.
Light twins do not normally have sperate steering it is done through the nose wheel and braking and the engine help in the turn.
Aircraft from the commuter size seem to be the first aircraft to have a steering wheel or tiller (A Twin Otter has a tiller this is like a column change gear stick in a car up to turn right and down to turn left).
Sometimes controllers put pressure on pilots to do a tight 180 degree turn on the runway which does put a strain on the near undercarriage leg, an Aurigny Air Services ATR went into engineering with in the last week with a cracked undercarriage some tight turns may have caused or not helped this.
Our runway is 46 metres wide the turning circle i understand for a Boeing 757 is 45 metres so you have not got a lot of room either side, aircraft have gone farming before now by turning on the runway and going over the edge.
Not only the pilot being red faced but the controller could take some of the blame by better use of the taxiways or dumbell turning circles at the end of some runways thats my oppinion any way.