The information here is written about the iPhone but other 'phones/platforms have some of the same or similar functionalities - or will have.
The built-in Google Maps and GPS apps work together really well. Google Maps brings the map, satellite and Street View functions - just like on a normal laptop or desktop computer.
With these you know where you are can also plan trips (Google doesn't know where most cycle paths are, but is apparently working on it).
For high quality cycle journey planning you need Cyclestreets - or even edinburgh.cyclestreets. This is not a standalone app (one day, maybe) but is a web one which works with a normal web browser.
On the iPhone this is Safari and it's easy to use - just touch the screen for start and finish points, press "Plan this journey" and see a choice of three routes (fastest, balanced, quietest) displayed in seconds. The programming is being done in Cambridge, partly funded by the Scottish Government.
Your planned route come with its own web address (URL) e.g. http://edinburgh.cyclestreets.net/journey/93085. A GPX file can be downloaded to use in GPS devices (and/or a KML file for viewing in Google Earth).
In addition a link can be made to the GPX file (e.g. cyclestreets.net/journey/93085/cyclestreets93085.gpx) which can be pasted into the iPhone app Trails Lite (free) and the iPhone used to track the route. The full version of Trails costs £2.39.
One reason for upgrading is that you can store more than one route on the iPhone. Another is that the Lite version only allows five minutes to record a new trail - but Everytrail (see below) is probably better unless you want to compare your new route directly with a previously recorded route (which might be a good idea if you are exploring somewhere new to you).
The underlying map data comes from OpenStreetMap which is an open source map that anyone can add to or (where necessary) correct. It's even possible to add useful details (POIs - Points of Interest) using Apps.
lLOE - iPhone Little OSM Editor is available for 59p and Mapzen (from CloudMade) is expected in the AppStore in a couple of weeks - register now for info or use the normal computer version.
One really great app is currently suffering from its popularity. IOSMaps puts real Ordnance Survey maps on your iPhone screen for free. Unfortunately due to daily data restrictions this 'runs out' quite early in the day. This may change with plans to open up access to 'our' data.
If you just want to record your trip - for personal use or sharing - the best app is probably Everytrail (free) already well established on the web and available as an iPhone App and also for Android, Windows Mobile, and Blackberry 'phones.
Not only does it record your trip (on the iPhone it may be necessary to run the iPod in the background so the app doesn't go to sleep!) in a form that can be exported and used in other GPS devices (or used for OpenStreetMap) you can take photos along the way which will appear on Everytrail.com (if you choose) or can be used by themselves.
Another app which records your travels is FirePin (free) (also for Android). You can email a link to people even before you set off so they can follow your progress. Useful for letting people know when to put the kettle on...
One of the few problems with iPhones is battery life. Considering all the things that they do I think battery life is good - better than most laptops in terms of hours of use. I have recently bought an add-on battery which will recharge the iPhone for a few more hours of use (it can be used while charging).