See line breaks and carriage returns in editor

Assuming your vim settings for :set listchars=... is set to visualize the characters you are attempting to see, in this case the carriage return characters (typed with CTL + V, CTRM + M) —— otherwise, as reported in many of the comments on this answer, the ^M character will not show on :set list

:set list in Vim will show whitespace. End of lines show as '$' and carriage returns usually show as '^M'.

To disagree with the official answer:

:set list will not show ^M characters (CRs). Supplying the -b option to vi/Vim will work. Or, once Vim is loaded, type :e ++ff=unix.