Use wc:

wc -l <filename>

This will output the number of lines in <filename>:

$ wc -l /dir/file.txt
3272485 /dir/file.txt

Or, to omit the <filename> from the result use wc -l < <filename>:

$ wc -l < /dir/file.txt
3272485

You can also pipe data to wc as well:

$ cat /dir/file.txt | wc -l
3272485
$ curl yahoo.com --silent | wc -l
63