Messaging Hosting ??? | Talk Web Hosting

I have not seen any forum for this, so I thought of posting it here (Mods: Please, move this thread if necessary)

I have 2 areas that our company mainly uses for email, so web hosting for these areas is not necessary.

Is there a company specializing in hosting e-mail? This comes with security alerts to our emails will be accepted everywhere?

We do not do mass mailing, we only respond to incoming requests for new customer information and technical assistance from existing customers.

If anyone has any leads on a good service to provide for email hosting, please let me know. Thank you!