Free sites are primarily effective for general research (i.e. cities, courts, cases, etc). The advantage to using a free site is accessability and a lack of commitment (i.e. no membership dues or giving of email information, etc) but you may find limitations in both what you can find and the ease at which you find it.
Free sites are a good place to start for information finding. For instance, if you need to find a person a good free site to start with is the Yahoo People Finder but if you do not have success and feel there is information on a person you should try a paid site such as Lycos People Finder.
A good deal of judicial / governmental information (i.e. court forms, case information, court opinions, FOIA, etc) is available from free sites and should not require any paid service.
Paid Sites are effective for more specific and/or difficult information. The advantage to using a paid site is quality. Paid information services such as Choice Point, Query Data, and Lexis Nexis charge you for their services but the information they provide would be either very difficult or impossible to find through a free site.
If, for instance, one should need
Basically, if you think the information you are looking for is public and listed somewhere try a free site. If some amount of prying, research, or extra time may be involved (i.e. DMV records, Death records, etc) a paid site might be your only option.