There is no such thing as a free lunch nor a free tld (Top Level Domain
)Someone, somewhere, will pay for it and usally you will.
When advertising for free domain names offers popup, often,owners / users pay
for that free name in some fashion or form.There is always a catch to having a
free domain name.
The issues to consider a free domain offer are:
1.Is it a a subdomain or a real domain? The physical
difference is
http://www.yourdomain.com vs
yourfreedomainname.youmustpayforthis.com. The first one is easier for
users remember(if you have a hard time reading it how the heck can you remember
it?). You would own yournewdomain.com, but who every own the
"youmustpayforthis.com" part of the free domain name offer would own the
subdomain part too.Having Ownership of a real top level domain is one of the
most important issues to any websites success.Most fail to realize this fact
untill its too later and some one else(the owner of youmustpayforthis.com)
decides to take your traffic generated by you now popular FREE subdomain
name.Buy a domain for your website and the future success of your online
business won't be hampered by a lousy,free subdomain domain.
2.A lot of the real free domains are offered by web
hosting co. Hosts will offer free domains with a web hosting plan. Be careful
signing up for such service. You may end up with a free domain but a year's
worth of junky web hosting service. The best advice is to keep your website
hosting and domains register with different companies.But not all webhosts are
out to get ya either 
3.Consider naming your website so others know by seeing your
new domain name what your website is about.