You can still cache maps, sort of, but it's like carrying a mapbook which may, or may not, spontaneously disappear at any time. Not much use in a pinch, is it?

OSMAnd has been mentioned. I am a huge fan of Locus, as it seems more polished and the author is always adding cool new features. Both are good apps for Android (and may have i-versions? not sure).

If you go the offline route, don't miss these custom hiking and biking maps: openandromaps - Hike'n Bike maps for Android (site seems down at the moment)
They are based on the openstreetmap data but with special additions and themes just for cycle tourists and other outdoor recreation.
Be sure to support the project with a cappuccino (or more)...