- Google Maps (built-in) - indispensable for maps, routing (driving, walking and especially public transport) and Street View.
- OffMaps - download maps on wifi in advance, for offline use; now includes some routing.
- RouteBuddy Atlas - OpenStreetMap, OpenCycleMap and purchased Ordnance Survey maps (though they're really expensive).
- iTrail - record GPS tracks (just remember not to switch the screen off; not sure if this is still the best of its kind, I haven't looked at the others recently).
- Yelp - brilliant for restaurants
- Showtimes - cinema listings
- beeloop "At A Glance" City Guides - I like the "What to do now?" feature, though only the San Francisco version is free. It could do with reasons why places are recommended, too.
- Dopplr - the best presentation of all the "nearby" apps so far, but doesn't have many places listed yet. Also good for adding data, with the "I've been here/I liked it".