The short answer to this question is no, you can not use the Web to find free birth records. This kind of information is generally not stored online for public access. In addition, each state and country usually have their own specific guidelines on the process you need to follow in order to obtain birth records. Bottom line: you can't find free birth records on the Web, and anyone who tells you who can is selling you a load of baloney.
However, there ARE sites that give you the information you will need to start tracking down those birth records, for whatever state or country you may be in. The best one I've found for this purpose is VitalRec.com.
VitalRec links directly to each state and country's information on EXACTLY how to obtain vital records: birth certificates, death notices, marriage records, and more; plus, VitalRec has a detailed set of guidelines for ordering these records with all the information you need to include in your request.
No, you can't use the Web to find free birth records, but it is a good starting point to help you in your search.
More help with public records