While you may also be having a firewall problem as stonux suggests, Sendmail by default only accepts email from local users (on the localhost or lo interface). To change this, you will want to do the following as root:
1) BACK UP the contents of /etc/mail... just in case =
2) Edit /etc/mail/sendmail.mc
a) Look for a line that looks like this:
b) Add dnl (which stands for 'do not load') to the beginning of the line so it looks like:
dnl DAEMON_OPTIONS(`Port=smtp,Addr=127.0.0.1, Name=MTA')dnl
3) Run the command 'm4 /etc/mail/sendmail.mc > /etc/mail/sendmail.cf'
4) Run 'service sendmail restart'
If you get an error during step number 3 about not being able to find sendmail-cf or something to that effect, install the sendmail-cf rpm off of your RedHat CDs or run 'up2date sendmail-cf' if you have up2date set up.
Here's what those instructions have you do -- The config file that sendmail actually uses is called /etc/mail/sendmail.cf, but the syntax for that file is... wierd, to say the least. To avoid having to modify it by hand, the file /etc/mail/sendmail.mc is provided. This file is written in a special macro language called m4, which is supposedly easier to read and modify than the original sendmail.cf. When you run the contents of sendmail.mc through the m4 interpreter (step 3) it interprets those macros and produces a sendmail.cf file. Normally it would spit the new file's contents out to the sceen, but the '> /etc/mail/sendmail.cf' redirects it into a file instead. The modification you made to sendmail.mc and then translated into a new sendmail.cf simply tells sendmail to ignore the line that would normally instruct it to only listen on the local interface. When you restart sendmail (step 4) it re-reads your new sendmail.cf and should accept mail from anyone.
If you're going to run sendmail, do make sure you've got it all up2dated so that you're using all relevant security patches and set up a firewall unless you really do intend for *everyone* to be able to access this service.