How can I clear the current line of the Windows command prompt?

The Escape (Esc) key will clear the input line.

In addition, pressing Ctrl+C will move the cursor to a new, blank line. This may be helpful as the input you just reviewed remains visible while you type the new command.

Aside from the two that Myyrddin covered - Esc and Ctrl+C - there are also two more shortcuts related to clearing the current input in CMD.

Ctrl+Home will clear all characters in the input before the cursor (equivalent to Ctrl+U in Bash)

Ctrl+End will clear all characters in the input after the cursor (equivalent to Bash's Ctrl+K)

Both are fairly useful and, once internalised and gotten used to, could speed up editing in CMD by quite a bit.