Unfortunately, there are too many types of phones to list. You can check if your phone can be charged by the WakaWaka Power+ by checking its battery capacity.
The WakaWaka Power+ (product code WP22) has a battery capacity of 2200 mAh. In order for the WakaWaka Power+ to fully charge your device, its battery needs to be around the same amount or less. For example, the WakaWaka Power+ cannot fully charge the Samsung Galaxy S5, because the battery is simply too big. But it should fully load your Iphone 5s since it has a battery of 1570 mAh.
The Power+ (s/n P02Axxxxxx) has battery capacity of 3000mAh. Therefore this Power+ can charge devices with bigger batteries.
Furthermore, it is important to note that your device will charge from a WakaWaka at approximately the same speed as from its grid charger.