What to play with your 360 degree wheel:

MAME

American Speedway (set 1)
APB - All Points Bulletin (rev 7)
Bad Lands
Buggy Boy/Speed Buggy (cockpit)
Buggy Challenge
Change Lanes
Chase H.Q. (World)
Championship Sprint (rev 3)
Double Axle (US)
Demolition Derby
Drag Race
Fire Truck
Grand Champion
Grudge Match (prototype)
Hot Rod (World, 3 Players, Turbo set 1, Floppy Based)
Danny Sullivan's Indy Heat
Konami GT
Monte Carlo
Night Driver
Night Stocker
Ironman Ivan Stewart's Super Off-Road
Ironman Ivan Stewart's Super Off-Road Track-Pak
Pole Position
Pole Position II
Redline Racer (2 players)
Road Blasters
S.C.I. Special Criminal Investigation
Sprint 1
Sprint 4 (set 1)
Sprint 8
Super Sprint (rev 4)
Stocker (3/19/85)
Street Heat
Subs
Super Bug
Top Secret
TX-1
Wheels Runner
Virtua Racing

270° wheel games which also work with a 360° wheel:

A.B. Cop
Ace Driver
Aqua Jet
Big Run
Blomby Car
California Speed
Chase Bombers
Cisco Heat
Continental Circus
Cruis'n USA
Cruis'n World
Cyber Cycles
Dirt Fox
Driver's Edge
Enduro Racer
F1 Exhaust Note
Grand Prix Star
F-1 Grand Prix Star II
Final Lap 2
Final Lap 3
Final Lap R
Final Lap
Four Trax
Ground Effects / Super Ground Effects
1000 Miglia: Great 1000 Miles Rally
Mille Miglia 2: Great 1000 Miles Rally
Hang-On
Hang-On Jr.
Hard Drivin'
Hyper Crash
Hot Chase
Hyperdrive
Max RPM
Midnight Run
OutRunners
Out Run
Power Drift
Pocket Racer
Race Drivin'
Racing Hero
Radikal Bikers
Rad Mobile
Rad Rally
Rave Racer
Ridge Racer
Rough Racer
Round Up 5 - Super Delta Force
Stadium Cross
San Francisco Rush
Super Hang-On
Shot Rider
Side By Side
Side By Side 2
Slip Stream
Super Monaco GP
Speed Racer
Speed Up
Spy Hunter
Spy Hunter 2
Super Chase - Criminal Termination
Suzuka 8 Hours
Suzuka 8 Hours 2
Turbo Tag
Ace Driver:Victory Lap
WEC LeMans