Is UL approval required on all items sold in the USA
The National Electrical Code requires that all items installed in a building be tested by an NRTL, generally that means UL listed. This does not apply to your personal use items, but does apply to any fixed appliances or electrical equipment that is installed within your home or commercial facility. If your local jurisdiction has adopted the national electrical code then this requirement applies.

Maybe...  Assuming this is a mains powered device?  There is US Federal law and there are also local laws.  If you only sell a few you may get away with not getting a Nationally Recognized Testing Laboratories (NRTL) approval (there are many NRTLs, UL is just the most well known).  However, besides pingswept's point, local electrical inspectors may prevent business owners from using your equipment based on local regulations unless they see an NRTL mark (even though the Federal gov may not require it).

Check with the test house that did your CE approval, if they are big enough they may also grant NRTL marks (we use TUV Rheinland).  Note that not using UL or CSA may cause problems in some jurisdictions that are old fashioned.  We have a $4.5M medical device and the City of Baltimore wanted UL, CSA or MET Labs so we gave MET Labs the TUV test reports and a check for a few thousand dollars and they gave us an approval.  UL is a pain to work with, I would go with CSA before UL (even though CSA is Canadian they can grant US NRTL marks in general).  Also note that as part of getting an NRTL mark, you will be signing up for periodic (typically four times a year) factory inspections where the NRTL will make sure you are still building your product in the approved way.  Of course you pay for that privilege.

http://www.greenexpo365.com/portals/asf0001/resources/intertek/The_Q&amp;A_Guide_for_NA_Product_Certification%28US%29.pdf

I think the bottom line for mains powered equipment is, if you want the US to be a significant market, you want an NRTL approval.  While getting the NRTL approval, throw in the Canadian approval, there are only small differences in the requirements and you open up both markets.

Eric