I debated the same question a little while ago and eventually bought a FZ18. Reasons:
The 18x zoom is astounding. To get an equivalent lens with a DSLR would cost much wonga.
A bottom end DSLR costs more than the FZ18.
A DSLR rarely has an LCD display, just a normal viewfinder.
The FZ18 has an huge array of user-friendly settings including a superb Intelligent Auto mode which is so useful since if you're taking a bunch of shots in one session, some portrait, some macro, some landscape etc. it sorts it all out for you without you needing to bother with any 'advanced' settings. In my opinion this gives it far more versatility.
The movie mode on the FZ18 is excellent although zoom is disabled when filming.
Of course, it depends on how far you want to delve into advanced photography. A DSLR will generally give you a better quality photo but of course this depends a lot on the photographer. Also you have a whole variety of lenses you can use with a DSLR, (at an extra cost of course).
It's a tricky decision but in the end it comes down to justifiable cost.
Personally, I'd recommend the FZ18 as a great camera.