terminal: count all files - including in sub folders

find DIR_NAME -type f | wc -l

Explanation:

-type f to include only files.
| redirects find command's standard output to wc command's standard input.
wc (short for word count) counts newlines, words and bytes on its input (docs).
-l to count just newlines.

Notes:

Replace DIR_NAME with . to execute the command in the current folder.
On some systems (e.g. OS X) you can omit . for execute in the current folder
You can also remove the -type f to include directories (and symlinks) in the count.
It's possible this command will overcount if filenames can contain newline characters.

Pro tip:
If you want a breakdown of how many files are in each dir under your current dir:

for i in */ ; do echo -n $i": " ; (find "$i" -type f | wc -l) ; done find . -type f | wc -l

folders:

dir /a:d /s /b "DIR_PATH" | find /c ":"

files

dir /a:-d /s /b "DIR_PATH" | find /c ":"

On window you can omit "DIR_PATH" with . too.