Short answer – YES!
Some states follow the ABA Model Rules of Professional Conduct and strongly suggest, but do not require, that all engagement agreements be put in writing. (For example, ABA; Georgia; Alabama; Illinois).
And most, if not all, jurisdictions require contingent fee agreements to be in writing. (For example, Georgia).
Even if your local rules do not dictate that a particular engagement agreement be in writing, it is advisable that a lawyer not begin any substantive work on a new matter unless and until the client has executed an engagement agreement. This is true even for existing clients.
The engagement letter sets expectations and ground rules and helps avoid misunderstandings. Done correctly, it will ensure everyone is on the same page.
Putting the terms of the engagement in writing aids law firms in their risk management and should help minimize potential liability down the road. Indeed, the engagement letter is often the first line of defense whenever there is a dispute between a lawyer and client, and it could be the determining factor in defending a malpractice claim or bar grievance.
So send every client a written agreement for each engagement, no matter the size. And GET IT SIGNED.