I use Navigon. It's expensive for an iPhone app, but worth it IMO. It works without GPS and works just as well as a much more expensive (if we're talking about the price of the app, not the iPhone, which you already have anyhow) dedicated GPS. I've used it for probably five thousand miles of car travel and probably six to seven thousand miles of bike travel. One big downside to Navigon is that it will sometimes freeze up or quit working and require a restart. Fortunately, this only happens minimally. Also, once you've chosen a route, if you deviate from that route, it will give you directions to get you back onto that route, rather than give you the newest 'fastest route.' If I get far enough off of my route for whatever reason, I just cancel the directions and have it renavigate. Navigon isn't perfect, but it's damn good.
I used to have a crappy bicycle mount that I used for the iPhone and would have thick rubber bands around it to keep it in place. I did a 1700 mile trip, some of it in the rain (with the phone in a ziplock bag), with it in that holder. It worked beautifully. I recently bought a new bike mounted case for it. It is a case made by Ultimate Addons
that I bought from Amazon. It is designed for the iPhone 3G/GS, but they also sell one for the iPhone 4/4S. It is waterproof (I tested this with a hose and not a drop got in) and allows a charger and/or headphones to be used with it while maintaining its waterproofness. I tested this out with a charger, but not with headphones, as I don't use them while riding. The touchscreen works while it is in the case perfectly - huge plus! I will say that I haven't had this setup for very long and can't speak of its durability/longevity. I will say, however, that it feels really solid, and I don't anticipate any problems with it. Here are some pictures of it mounted to my bike.
It is designed to be mounted to a motorcycle's handlebars by replacing one of the handlebar clamp bolts (and replaced with one from the kit). My bike has clip-ons instead of handlbars and thus doesn't vertical handlebar clamp bolts. It does, however, have bolts that are attached vertically that hold the triple tree to the forks. I cut down, smoothed out, and re-drilled a stainless steel bracket to overcome this problem.
I then attached the bracket to the triple tree bolt and then attached the mount to the bracket. It works perfectly.
The mount can rotate 360 degrees and can tilt nearly vertical in all directions. There is more adjustability than could possibly be needed.