I've been using my trusty
Braun 3D Excel for years now, and I've never had any problems with my teeth (I have the "
Oral-B ProfessionalCare® 7550" model). It is an electric toothbrush with a 2 minute timer, so my brushing sessions are generally fairly consistent in length. I haven't really used many electric toothbrushes, but in comparison to those I've seen/used, the 3D Excel (7550 model) is by far the most powerful/efficient. Based on the results I've gotten from it (you can't argue with having no teeth problems), I'd recommend it to anyone.
The only reason I'd get a new toothbrush is to update to the "Oral-B ProfessionalCare® 7850 DLX" model, which has a 30 second timer so you can ensure you're spending an equal amount of length brushing all areas. My current model only has a timer that signals at the 2 minute mark. Granted, I could use a watch or a kitchen timer to time in 30 second increments, but I prefer the luxuary of having the timer in-built into my toothbrush (it signals by stopping the brush head from spinning and then starting it again, and it does this 3 times, which is quite effective; you always know when the timer goes off).
As for dentist checkups, I haven’t been to a dentist in years simply because I don't need to -- I've never had anything wrong with my teeth, and after hearing what others have experienced from dentists (I won't go into detail, but it's nothing good), I can definitely find a better thing to do with my money/time. People may think that I'd have a lot of problems with my teeth because I never get a check-up, but I've found it to be quite the opposite -- those who go to the dentist seem to get/have more problems then I do (which is pretty easy to do, since again, I've had zero problems).
I don't know exactly why this is (the Law of Attraction at work, dodgy dentists, poor dental care on the behalf of those who visit the dentist), but I'm sure not going to argue with the results. I will note, however, that like in many areas of my life, I have this underlying belief that my teeth are in top condition and that I have no problems. To the degree this has influenced my results, I don’t know, but again, so long as that belief serves me, I’m not complaining; quite the opposite -- I'm very grateful.
In terms of toothpaste, I’m still using toothpaste that contains fluoride, but based on
what Steve has said about fluoride, I’ll be doing some research in the near future to see whether or not that’s a practice I’d like to continue. Toothpaste seems to be pretty much all the same -- it either has fluoride or it doesn’t. I will mention that I’ve never used any gel toothpastes. The, errr... non-gel toothpaste is what I used when I was younger, and I’ve continued that habit ever since because I’ve seen no reason to make the switch to gel.
Based on my experience, I think the best dental advice I could offer would be to focus on logical prevention (Steve also advocates a similar approach for dental care in the
article I linked to above). What do I mean by that? Focus on intelligently preventing problems by not focusing on problems, and instead focusing on solutions that will prevent them from arising in the first place. You can spend all the time in the world trying to get rid of the weeds (the symptom/s of the problem), but until you pull out the roots (address the cause), you'll never be rid of them. And because the following quote sums up my point so elegantly, I just had to include it (and I also find it amusing that I managed to fit a Sun Tzu quote in a post about dental care

):
When you know your enemy and know yourself, you
need not fear the result of a hundred battles.
~ Sun Tzu
Edit, 14 August 2008: I've now transitioned to a natural, herbal, fluoride-free toothpaste. I've been using it for a few months and have no issues to report.