There is no way to remove everything from the entire internet because servers have copies of other servers, and many places (without legal action placed against them for a real reason) will not remove things even if you ask. If you are lucky, contact individual sites where you have information records and ask or check their policies-- but all are of course independent of each other and different in what they allow.
Reputation.com claims to have a large effect, but I cannot be sure of their (and therefore your) results at all.
There is also the possibility of legality of public records. If you have public information for any work you have done or anything in public [sport, events, exhibits...] it is very possibly posted.
There are also the possibility of legal records. If you are in the United States for example, and people know which state you are in, and you get so much as a traffic ticket, it is often live on a public access site. People may have to know more information to find it, but it can often be found for free and a little research.