Some of the problems you will come across can be seen in this pair of doors.

The hinges are too far over on the top resulting in a binding, out of parallel joint and there is also an alignment issue on the height, all of which can be resolved with a few turns of the driver.

If the door has a step against the next one...

But is parallel on the closing gap it can be resolved by altering the hinge plate.

Loosen the screws on the back plate enough to allow the plate to slide.

This will allow the plate to move up...

and down to lift and align the doors horizontally.

If the doors appear twisted when they are closed or are binding on the carcases the position of the hinge on the plate needs moving forwards or backwards.

The screw to adjust this is the one at the back of the hinge, nearest to the back of the cabinet.

On the more basic hinges this is simply a locking screw that is slackened to allow the hinge to move in and out on the plate. This screw also secures the door so it needs to be nipped up tightly after any adjustments.

The better quality hinges use a cam behind the screw to move the hinge along the plate and don't need tightening to secure them as the clip mechanism secures the hinge to the plate but each type follow the same principle.

The next adjustment is to counteract issues where the doors don't sit parallel to each other or to end panels.

The adjustment for this is done with the second screw on the hinge, the one nearest the edge of the door.

Tightening or slackening this screw jacks to door across to move the hinges fractionally.

On the more basic hinge you may need to slacken or tighten the rear screw that secures the hinge to the plate. It takes very minimal adjustment in most cases to get the door back in alignment. 

To get this door back in alignment the top hinge needed to be pushed out by tightening the jacking screw to stop it binding and the bottom hinge jacking screw slackened to bring it back in and make the joint parallel with good clearance.

After making all the relevant adjustments the result should be doors that sit perfectly aligned to each other.