I've had a GS3, a GS4, and now a GS5. The 3 and 4 would charge with any USB charger. Only the charging rate would change. I did some experiments with an old cable and found that the thin wiring in the cable was the culprit of the slow charging. When you get a phone (or tablet) with a 2 amp capable charger, it will be supplied with a cable capable of carrying that much power without a large voltage drop. If you have a lightweight USB cable, the voltage drop in the cable itself will drop below the 4 volts needed at the phone for proper charging.
I have a couple of built-in wall outlet 2 amp capable USB chargers. They charged the S3, S4 and older tablets just fine. Now I have an S5 and just got a Samsung 10.1 pro tablet. Both refuse to charge from the universal 3 amp chargers. They will charge from only the original Samsung chargers or from my laptop. Samsung has changed something in their charging circuits recently. I think if they detect a non-samsung charger they just refuse to charge completely instead of just defaulting to a slower rate. Does anyone know if this is fact or a way I can mod my wall charger to work on the new Sammy devices? I don't mind slow charging.