Worn inner and outer tie rods (inners are integral to the rod, outers are "ends") will absolutely give that loosey-goosey feel.

Assuming that all the tires are at the right pressures and the road you are driving on has no appreciable crown, you should be able to let go of the wheel and travel for move than 5 seconds in your lane. A particularly low tire will cause an aweful pull...as will a damaged tire (seperated belt) or poor alignment.

After that, place two fingers on top of the wheel and see if you can move it while driving. If it moves more than about an inch in either direction without changing direction, have the tie rods and ends checked.

Onkel Udo