I have been using Yahoo Groups (groups.yahoo.com) for mailing lists,
but it has a fatal flaw: it requires people to create a Yahoo ID if
they don't have one. That significantly reduces the number of people
joining my list.

Is there another solution which is easier to use for the list-member?
And preferrably, it should be free.

Thanks

Dear Atr, 

Google Groups* also enables you to found a group. A person should also
have a "Google Account", but that doesn't mean that these people have
a Gmail account (or have a Gmail mail):

Google Groups - Create a New Group
<http://groups.google.com/groups/create?lnk=l&hl=en> 

Topica also offers this service : 

Topica - Start a List
<http://lists.topica.com/create/index2.html> 

Here are several more places to consider: 
The Free Country: Free Mailing List Hosting and Email Newsletter Hosting 
<http://www.thefreecountry.com/webmaster/mailinglists.shtml> 

Free Email List Hosting Services
<http://www.emailaddresses.com/email_mailing.htm> 

Freelists
<http://www.freelists.org/> 

I hope this answers your question. Please contact me if you need any
clarification on this answer before you rate it. My search terms:
Search within Google Groups and Topica (personal knowledge)
[Free Mailing List Hosting Service] 

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* May I note here that Google Answers Researchers are not Google
employees and we get nothing from recommending a Google Service.