A local web-dev company has been using the Apache-Tomcat combo for a while now. Most of their existing work has been trad Perl/cgi, but they are doing most of the new stuff with servlets/jsp. The don't particularly have hi-traffic sites, but they do have many sites being hosted by the same server. To my knowledge, Tomcat has never brought the system down.
Some other points: Tomcat is good, and it is free, but it is a pain to maintain and configure. Getting it to work and getting it to work WELL are two very different things. And administration? Granted, it is like a lot of Unix type systems and needs little maintainence once set up, but if it does, you REALLY need to know it well. But you can't beat the price. If you have the resources, I highly recommend JRun Server Professional. It can be installed to run with Apache on a Linux box in about 10 minutes. I has web based admin. I also has a lot of cool features like maintaining DataSource objects (pooled database connections in a naming service). It has a free dev license if you want to play with it.
Basically though, if Tomcat is not stable or performing well, it's probably your fault.
As a side note, a friend of mine is a professional servlet developer. The front end, i.e., html is done in a seperate shop. She just hands them the jsp tags to use to get the dynamic content into their pages, and it makes for a very nice, clean separation. You CAN put all the java code in the JSP, like you do with ASP, but this way you don't have to worry about someone fat fingering the script that they pasted into their page.
chris