Which airport is the busiest general aviation airport in the world?
US
According to General Aviation News in Feb 2020 that would be Van Nuys in California.

Van Nuys Airport (KVNY), Van Nuys, California: 155,420 local GA operations + 332,117 itinerant GA operations = 487,537.
Phoenix Deer Valley (DVT), Phoenix, Arizona: 130,886 local operations + 243,075 itinerant = 373,961.
Centennial Airport (KAPA), Denver, Colorado: 153,744 local operations + 133,098 itinerant = 286,842.
Ernest A. Love Field (KPRC), Prescott, Arizona: 177,233 local operations + 85,290 itinerant = 262,523.
Long Beach Airport-Daugherty Field (KLGB), Long Beach, California: 151,912 local operations + 101,734 itinerant = 253,646.
Portland-Hillsboro Airport (KHIO), Portland, Oregon: 160,261 local GA operations + 83,381 itinerant = 243,642.
Phoenix-Mesa Gateway Airport (KIWA), Phoenix, Arizona: 166,519 local operations + 66,727 itinerant = 233,246.
Falcon Field (KFFZ), Mesa, Arizona: 175,051 local + 53,307 itinerant = 228,358.
Grand Forks International Airport (KGFK), Grand Forks, N.D.: 212,325 local + 12,634 itinerant = 224,959.
Gillespie Field (KSEE), San Diego/El Cajon, California: 140,189 local + 68,061 itinerant = 208,250.

Source: https://generalaviationnews.com/2020/02/03/top-10-busiest-general-aviation-airports/
Anecdotally; although not American, I just realised I learned to fly at the 5th busiest GA airfield in the US. Mind blown! 
UK
Contrast this to the UK, which has a fairly busy GA scene:

Official Civil Aviation Authority statistics have revealed that Gloucestershire Airport at Staverton was amongst the busiest in the UK during 2011, with the majority of the traffic being GA aircraft  [...] Gloucestershire appears at number 13 in the list of 64 UK commercial airports, handling 66,715 flights during the year -- just pipping Bristol and beating other major regional airports such as Newcastle and Belfast.

As you can see the UK's busiest GA airfield doesn't even come close to the US' 10th busiest.
Australia
Not so easy to find a list, and there is more than one contender for busiest
Jandakot deems itself to be busiest by movements:

Jandakot Airport is &quot;the busiest general aviation airport in Australia in terms of aircraft movements&quot;. The airport recorded 208,778 aircraft movements in the fiscal year ending 30 June 2018

Moorabbin seems to be the busier by aircraft movements, and is clearly a strong contender.

With over 295,000 aircraft movements each year, Moorabbin Airport is the second busiest airport in Australia. [...] Moorabbin Airport is Australia’s leading general aviation flight training airport located in the south-east of Melbourne.