Guy Oldfield contributed this list of shuttle services between Phoenix Sky Harbor Airport and Casa Grande.

Arizona Airport Shuttles
(602) 381-1111
web site
Fare (shared ride) PHX to Casa Grande: $53.00 one way, $106.00 round trip
Extra person: $10.00 each way
I used this service twice. My only complaint was that I had a 2-3 hour wait at the airport each time. They were prompt to pick me up in Casa Grande.

J&M Shuttle
(888) 344-3937
Fare: With 24 hour notice, $55.00 each way, with less than 24 hour notice, $65.00 each way.
Extra person: $10.00 each way

Pinal Connection
(800) 427-1271
Fare: $55.00 each way, extra person $10.00 each way.