To show how many files and directories in the current (target)
directory:

 $ ls | wc -l

To count just files, and exclude directories, you could try
something like:

 $ find /target/directory -type f -print | wc -l

A quick, if somewhat ugly, way to do it, counting the dotfiles too:

 $ ls -aF | grep -v /$ | wc -l

Again, you can use the Unix tool for everything - grep:

 $ ls -F | grep -Ev '/$'|wc -l

Or, if you also want to exclude symlinks:

 $ ls -F | grep -Ev '/$|@$'|wc -l

How about:

 $ find /target/directory -maxdepth 1 -type f -print | wc -l

or:

 $ find /target/directory -type f -maxdepth 1 | wc -l

ls(1) which is terribly slow at displaying (actually at sorting)
large directories, is better off having the -f switch.
If you'd like to test the difference in how long it takes ls to
count files, depending on the switches you put on the end, try:

 $ time ls -f /usr/local/news/News | wc -l
         0.42 real         0.29 user         0.07 sys
    35935

 $ time ls /usr/local/news/News | wc -l
       147.02 real        33.92 user         0.07 sys
    35935

And ls -lf makes working with awk faster, too. E.g:

 $ ls -lf | awk '$8 == 2007 {print $9}'
 $ ls -ltf | awk '$8 == 2007 {print $9}'

If you've got  a large number of files, ls -lf is roughly
twice as fast.

Here's a more dramatic change in the time, using ls, awk & wc:

 $ time ls -lf | awk '$8 == 2006 {print $9}' | wc -l 
       15 
     0m0.07s real     0m0.06s user     0m0.01s system

 $ time ls | awk '$8 == 2006 {print $9}' | wc -l     
        0 
     0m0.04s real     0m0.00s user     0m0.03s system

I guess from my reading on the FreeBSD mailing list, there
may be some conjecture as to if you have a large number of
files, that ls -lf appears to be faster than just ls.

One person on the mailing list has said they find the most
intuitive way is to use something like:

 $ find . -maxdepth 1 | wc -l

where you can specify how many levels of subdirectories to
include in the count. Please note that count also includes
the current directory (".").

To exclude hidden files (.*), use

 $ find * -maxdepth 0 | wc -l

or

 $ expr `ls -l | wc -l` - 1