I have at last been dragged kicking and screaming into the second decade of the 21st century and have bought an iPhone !
So now of course I want to fill it with as many cycling apps as possible as recommended by you.
I would particularly like,
1 A speed / distance type thing
2 A GPS system that will show OS maps
3 A car like satnav for in town
any other amusing or useful apps with a cycling bent.

1: wahoo fitness
2: viewranger
3: no idea, Google maps seems ok on the odd occasion I need it.

Tomtom app is good for in the car (expensive).
OS App is good for……..OS maps (expensive).
Runtastic mtb is ok for short rides, but eats battery (cheap).
STRAAAAAAAAVVVVVVVVAAAAAAAA!!!!! (Free, but addictive)
If you have a road bike, bike fit fast is good for fitting, particularly if you have more than 1 (cheap).
If you build/true wheels, spoke tension gauge is vaguely useful (free).
Singletrack for reading singletrack magazine.

Road ID. Notifies loved ones at start/end of rides. Let’s them track you if you want and, will push ICE info to locked screen incase you’re found and not in a fit state to communicate.

Porn.

Outside. Free OS maps