Here are some of the things he worked on:
1) Factoring Polynomials over large finite fields (See here from 1970)
I quote the abstract
This paper reviews some of the known algorithms for factoring polynomials over finite fields and presents a new deterministic procedure for reducing the problem of factoring an arbitrary polynomial over the Galois field GP(pm) to the problem of finding roots in GF(p) of certain other polynomials over GP(p). The amount of computation and the storage space required by these algorithms are algebraic in both the degree of the polynomial to be factored and the log of the order of the field.
Certain observations on the application of these methods to factorization of polynomials over the rational integers are also included.I think he meant what we would call polynomial time when he says algebraic.
2) Combinatorial Games. He co-wrote the classic Winning Ways For your Mathematical Plays with John Conway and Richard Guy. These books are like NIM on steroids. They are FUN and have some serious math in them. (My blog system thinks Combinatorial is not a word. It is wrong)
3) Combinatorial Games. He was very interested in Go via Combinatorial Games. I have an article (alas, not online) by him entitled Introductory Overview of Mathematical Go Endgames. There has been further work on this that is on the web, see here. I wonder what ERB would think of the ALPHAGO program.
4) Berlekamp-Massey Algorithm finds the shortest linear feedback shift register for a given binary output sequence.
5) Berlekamp-Welch Algorithm efficiently corrects errors in Reed-Solomon codes. (Berlekamp also wrote a book on Algebraic Coding Theory.)
6) I didn't know about his work in finance until I began writing this, but the following quote from Wikipedia is impressive
In 1989, Berlekamp purchased the largest interest in a trading company named Axcom Trading Advisors. After the firm's futures trading algorithms were rewritten, Axcom's Medallion Fund had a return (in 1990) of 55%, net of all management fees and transaction costs. The fund has subsequently continued to realize annualized returns exceeding 30% under management by James Harris Simons and his Renaissance Technologies Corporation.