Examples:

Assume y[n] and y(t) are respectively outputs corresponding to input signals x[n] and x(t)

1. The identity system y(t) = x(t) is of-course Memoryless
2. System with description y[n] = x[n-5] has memory. The input at any "instant" depends on the input 5 "instants" earlier.
3. System with description

  also has memory. The output at any instant depends on all past and present inputs.