Are there any other important (which means nationwide-operating and
with own infrastructure) courier services in the US besides UPS, DHL,
USPS and FedEx?

Dear Hookahey, 

Yes. TNT is also a national courier express service. 

TNT
<http://www.tnt.com/country/en_us.html> 

I hope this answers your question. Please contact me if you need any
clarification on this answer before you rate it.

Hi Politicalguru,

of course I know TNT but just did not think about it.
Nevertheless - if there are no more providers... 5*

Thank you!