It would depend on the crime. If it was a minor misdemeanor, the judge at a minimum would require a parent or guardian. Anything more severe, the court will supply counsel. The one time a step daughter of mine got it trouble, she was provided an attorney. That was for malicious michief and destruction of private property. Of course with any legal question, a lot depends on your local and state laws. Reading your question again, the actual answer would be no.
A 14 year old is not legally able to enter into a contract or make other binding legal decisions for him/herself. Many laws give rights to adults that are not permitted to children. The Constitution also gives the right to vote to all - but you have to be a legal adult.
The Sixth Amendment says that defendant have the right to an attorney, a right which has been clarified by a number of key supereme court decisions (most notably, Gideon v Wainwright).
The right to represent yourself was not clearly established until 1975, with the case of Faretta v California. The Supreme Court has carved out some exceptions, such as when the state belives the defendant is not competent (Martinez v California, 2003). Public opinion was swayed be cases like Colin Ferguson, who was allowed to represent himself even though it seemed clear that he was insane.