http://www.bubbanews.com/ has a free service with a 50MB/day limit  - that
includes headers, so don't browse any of the binary groups.
Their groups list is good (42,000+) and retention is better than most ISP's
(i.e. RR).  I can still get messages in this group back to Feb '05.
You might need a Credit Card to sign up.  I've had this account for years
and never have been billed.

Another option is http://news.astraweb.com/ .
I bought a 25GB block of downloads for fills my ISP doesn't get.  It's a
one-time charge of $10 and there is no time limit to use it.  I've had it
for over a month and yet to use 1GB.  Good thing is that they DON'T count
headers.  Good groups list (35,000+) and retention is about two weeks for
everything.

Google search for "usenet server" yields

http://freenews.maxbaud.net/

and 9 million others.

I'm using cox and having very few problems. Every so often there might be some
incomplete binary posts, but the problem is usually quickly fixed. I use
news.east.cox.net for my news provider.