I have an email account with my hosting package. Is there a web service that will allow me to view my emails from any web browser (to simulate a Gmail like experience). So far I only know how to do it via the Mac Mail app and my iPhone.
You can still use gmail and add your hosting email account as a POP3 account: http://mail.google.com/support/bin/answer.py?answer=13287
Check out mail2web.com
mail2web.com offers a variety of services, including our flagship mail2web Webmail service which provides secure and anonymous access to your POP or IMAP email accounts from any browser or hand-held device. With mail2web Webmail you can pick up your email from any internet enabled device from anywhere in the world.
You can install a webmail client to your webserver. Here are some clients you can look at: http://www.noupe.com/ajax/10-ajax-webmail-clients.html