Yes, Tomcat is used by companies (and other organizations) large and small for apps ranging from minor to major, and is commonly clustered to make heavy-load failure-resistent application server systems. I worked on one where we matched up 4 quad-core systems (16 Tomcat instances) with load-balancing and that's far from the biggest configuration you're likely to come across.
The primary difference between Tomcat and products like WebSphere, WebLogic, OC4J and so forth is that Tomcat doesn't provide the full
J2EE service stack. It lacks such things as EJBs, JMS, and so forth. However an awful lot of production work can be done with just the basic Servlet/JSP platform, and Tomcat is ideal for that, since it doesn't require the long startup times more typical of full-stack servers. Actually, a number of full-stack J(2)EE servers embed a copy of Tomcat within themselves, including the
JBoss and JOnAS server systems. In addition to Tomcat, there's also the jetty server, which is reportedly somewhat faster than Tomcat. JBoss and JOnAS use a plug-in servlet/JSP component architecture, so either Tomcat or jetty can be used within them.
Technically speaking,
no system based on the HTTP protocol can truly be MVC, regardless of server, language or platform. The reason being that part of the MVC contract is that changes in the model must reflect back to the view. HTTP is a request/response protocol, and is forbidden by its basic architectural constraints from making unsolicited posts back to the client. The best it can do is send back update information when it responds to the next incoming request.
A number of frameworks for doing "MVC" exist.
Struts is one of the oldest, but it was actually known as Model2, since it wasn't full MVC even within HTTP's constraints. The Spring Framework likewise has Spring MVC. About the most complete MVC you can get is offered by JavaServer Faces, which, when paired with a good set of AJAX tags, such as RichFaces, makes for something that isn't quite MVC, but gets about as close as HTTP will let you.