ORIGINAL: B.L.E.
All planes need rudder to do a coordinated turn.
The amount of rudder needed for a coordinated turn depends on the bank angle. A 90 degree bank is all elevator. A 45 degree bank is half elevator and half rudder. A 30 degree bank is 86% rudder and 50% elevator.
I use the ailerons to set the bank angle and then I use a mix of elevator and rudder to carve the turn. The ailerons should be neutral during the turn. If you have to hold ailerons to stay banked, you are not using enough rudder. If you have to hold opposite ailerons to keep the bank from increasing, you are using too much rudder.
Nice description of making the turn, but I'd like to modify it a bit. Whether you have to maintain aileron input in the bank depends somewhat on how much dihedral is in the wing; more dihedral will tend to bring the plane out of the bank, so you might have to hold a little aileron through the turn to maintain the amount of bank you want. And note that B.L.E. mentioned elevator input; this is to maintain altitude through the turn. If you just use aileron and rudder, you'll lose altitude in the turn. How much you need will depend on the plane, some have more "pitch coupling" with rudder input than others, requiring more elevator input to counter it.
Now you can see what "coordinated" means; it's the simultaneous inputs of rudder, elevator, and ailerons in correct proportion to make the plane track properly through a turn. How much of each will vary from plane type to type, and how sharp a turn you try to make. Just takes a bit of practice, it'll become natural.
Not to pick nits, but 86% + 50% = 136%. Can't have more than 100%.