Do I need filtering caps for a USB power supply?
Yes, put a cap in.  

You don't say what the IC is, but you should have at the very least a decoupling cap across the power rail near the power pins of the IC, e.g. a 100nF ceramic is a typical value (or 1uF, 2.2uF, etc are cheap/common nowadays)
Depending on the IC and if there are other components present, you may need one or more larger electrolytics as well (e.g >10uF, near the entry point for the power rail). The effects of not having at least the smaller cap present may range from working, the odd glitch to not working, so for the cost it's an easy choice.
Usually the IC should have an example circuit in the datasheet and advice on decoupling/layout.  

Have a read of any decent electronics book for detailed info on decoupling and why it's needed, or search here (plenty of answers that deal with this) or Google - app notes on board layout/design from places like Xilinx / Atmel / Microchip etc. are worth a read.