Who has right to be represented by counsel in a court?

I believe, among our constitutional protections is the right to be represented by an attorney in court. Is this always true? Is there a time when a court can refuse to allow one to be represented? Does it matter if it is a civil or criminal case? Is this considered our 'equal access to the courts'? I ask this because I was told by an attorney that in a civil case, one does not have the protected right to 'benefit of counsel', that it only applies to criminal procedure? Am I wrong to disbelieve this ?