Too often, an organization decides to create or obtain a mobile web site, instead of a mobile web service. The difference: the former is a collection of XHTML (or WML) pages; the latter is an intelligent combination of various mobile technologies including XHTML, SMS, location, J2ME, and even desktop web sites.
Mobile applications enable sophisticated interaction with the user, either on a push or a pull basis. Think about the difference between a desktop email application that checks the server for new messages, compared with an email web site that you have to think to check for new messages - but extend the difference in both scope and intensity.
For example, if you go to the MapQuest desktop web site and get a map or directions, you can send your map to your mobile phone. You get a link to a J2ME application - they even automatically detect your carrier, and your map will be available as one of the items in it.
The really nice thing here is I can use my desktop for what it is good at, and my mobile for what it is good at. This application is a combination of desktop web, SMS, and J2ME. Better would be to provide an option for a mobile web presentation of the map, which could also be sent to other devices via SMS.
Side note: I've got MIDP2 installed on my Treo 600, but it was not detected as a supported device. Some more work needs to happen here. Of course, the entire J2ME (and to some extent, BREW) universe has promised but not delivered true cross-device development, so this isn't terribly surprising.
Optionally, this map application could detect progress in the driving directions, seek out traffic, construction, food, and weather information for the regions ahead, and alert the user when plans ought to be changed. This sort of functionality goes beyond a simple website, and is definitely a useful mobile application.