There are lots of types of flat rides out there....I will do my best to list them here with some UK examples. I have also included any height restrictions the UK rides currently have in place.
​(correct at the time of publishing).  
If you want to see the list via Manufacturers then please click here!

CHILDREN

Jump Around
Manufacturer: Zamperla
?? @ Sundown Adventureland

Convoy
Manufacturer: Zamperla

Mini Ferris Wheel
Manufacturer: Zamperla

FAMILY

Rockin' Tug
Manufacturer: Zamperla

Disk'O
​Manufacturer: Zamperla

Tea Cups
​​Manufacturer: Zamperla:

Barnyard
​​Manufacturer: Zamperla
?? @ Drayton Manor Theme Park 

Barnyard
​​Manufacturer: Zamperla

Kite Flyer
​​Manufacturer: Zamperla

Samba Balloons
​​Manufacturer: Zamperla

THRILL

Air Race
​​Manufacturer: Zamperla
Air Race @ Drayton Manor

Discovery
​​Manufacturer: Zamperla