In older CPUs, a special register served to "accumulate" intermediate results. Modern x86 CPUs do not distinguish any longer between accumulator (eax) and other general purpose registers. However, there are still traces of eax' history as an accumular; for example, xchg eax, reg32 is a one-byte instruction, while all other pairs take two bytes.
There are still many instructions that are linked to specific registers, e.g. cmpxchg, imul/mul, idiv/div, enter, leave, jecxz, cwd, cwde, cdq, scas, lods, stos, movs, cmps, push & pop, daa, das, in, out, ins, lahf, sahf, call, ret, xlat, and those opcodes that start with AA.