It's mostly harmless in a nose wheel configuration. You quickly blow all tires and slide along the runway on your wheel hubs until the aircraft comes to a rest. Crosswind will make the experience worse, because at lower speed you have less rudder authority and the aircraft might leave the runway.
If only one side is locked you will risk a ground loop. Here it is best to step on the other brake so both cause the same braking force.
But this is peanuts when compared to a tailwheel configuration. Here the consequence is a headstand right after you put some load on the wheels, which can be right at touchdown when you come down with some sink speed. Depending on the speed of the aircraft when this happens and the length of the fuselage nose, the aircraft might even flip on its back. Now this is sure to ruin your day. I've witnessed this once with a Polish Yak-12 which landed on soft ground - nothing more. The pilot climbed out unhurt from his inverted position, but damage to the aircraft was extensive. This was the occasion when I learned the worst Polish cursing ever.
If only one side is locked in case of a taildragger, I am unsure what will happen first: Ground loop or headstand. Details depend on the wheel track and the attitude at touchdown. Be sure to touchdown at the lowest possible speed and with the highest nose-up incidence possible to increase the resistance of the aircraft against flippig over. Unload the locked wheel with ailerons, so you touch down on the working wheel only, but make sure that you do this with as little sideslip angle as possible. Flying a gentle turn while touching down will help - just place the touchdown point at the moment when the aircraft is aligned with the runway (I know - easier said than done).
Touching down on one main wheel of a taildragger with some lateral speed by sideslipping into the direction of the working wheel will quickly roll the aircraft into the direction of the lateral speed, which helps to unload the locked wheel but might end up in a three-point landing: One wheel, wingtip and fuselage nose. Again, this is sure to ruin your day.
That is what is colloquially called a "headstand" (Picture source)