One moment it's a phone in your hand. The next, it's a full-fledged turn-by-turn nav unit with an active internet connection. What happened? These apps, is what.
iOS
GOLD MEDAL: MotionX Drive
The first wave of iPhone turn-by-turn apps was expensive and luxurious. The second was cheap and barebones. Since, members of both classes have scrambled for the perfect balance: Relatively cheap and pleasant, or at least painless, to use. MotionX Drive is a good turn-by-turn app at almost any price, but at $26 ($1 + $25 yearly subscription) it's basically a steal. Occasional road-trippers can purchase a month of service for just $3, as many or few times as they please. $1, iPhone and iPad (for $3)
SILVER MEDAL: Navigon
Initially regarded as a premium nav app, Navigon started out competing against the likes of TomTom. Now, with new region-specific pricing, it's in the trenches with the MotionX Drives and CoPilots of the world. And it fares well! Unlike many others, its maps are stored locally, so navigation still works in no-signal zones. (This also makes the app huge.) From $20 (Eastern states) to $50 (entire US), iPhone
BRONZE MEDAL: MapQuest 4 Mobile
It's missing some of the features standard in most turn-by-turn apps, like a street-level view and traffic data. But! Huuuuuge but! It's free, and it does basic, dependable voice navigation, which is 90% of the battle with these apps. It's no Google Maps Navigation, but it's awfully close. Free, iPhone
Android
GOLD MEDAL: Google Maps Navigation
Did you expect anything else? It's turn-by-turn navigation made by Google and more importantly, a part of Google Maps. You get live traffic data, location bookmarks, satellite view, search along route and Google's killer Street View. Plus its powered by, duh, Google Search and has all the googley features you've come to expect like voice search and of course, being free. The only downside is that its navigation is sorta dependent on your data connection as opposed to being preloaded (though it does cache your route) and the GPS voice is terribly robotic (but it does do text to speech). Free, Android.
SILVER MEDAL: CoPilot Live
It's not free, but you only have to pay a one time fee of $20 which is significantly cheaper than similarly capable GPS navigation apps. Plus, CoPilot's GPS voice is actually sorta pleasant, POI search is smart and you get 3D and 2D maps (though the downside is they're not particularly attractive). If you do a lot of driving in areas where cell phone signal isn't great, paying 20 bucks for CoPilot isn't a bad option since maps are preloaded onto your SD card. $19.99, Android.
BRONZE MEDAL: Waze
Waze uses user-generated maps which aren't always perfect, but it's free and turns navigation into a "social" game where you can see other Waze users on the road and earn points by hitting landmarks. Not useful enough to be a full time GPS but fun enough for those times where driving gets boring. Free, Android.