Times New Roman and Computer Modern should not be used by anyone. I don't have a "rational" argument, but just look at them, they're ugly.
I do: Times New Roman was designed for a newspaper — Brittain’s “The Times” — which means it was designed in large part to keep the cost of paper and ink down. Compared to book fonts of the time, Times New Roman has uncommonly narrow letterforms and short descenders to allow for more text on a line and more lines in a column.
If you care more about aesthetics than about ink and paper cost, you should never use Times New Roman.
I second the recommendations for Garamond and Palatino.