Estimate the amount of time it will take me to circumnavigate the Earth on commercial airplanes. Assume I have enough money to purchase the tickets. Provide a flight plan.
First the estimation: it would take about 2.6375 days (or 63.3 hours), including about 1.8 days (43.2 hours) in the air and 0.83 days (20 hours) waiting for layovers.

My estimate for the amount of time required to circumnavigate the Earth commercially depends on a number of factors including the number of stops, duration of layovers, and the speed the airplanes travel at. I based my estimate on the following factors and assumptions:
- The speed of the plane, which I'll assume based on the average speed of an airline at 575 miles per hour
- The number of stops, which I'll estimate at about 5
- The average distance travelled for each route
- The duration of the layover, while I'll assume is an average of 4 hours per stop

Here let me express that mathematically so you can see my work:
Total Time to Circumnavigate the Earth on a Commercial Airline = 2.6375 days = 63.3 hours = (5 x (24,901 miles / 5) / 575 miles per hour) + (5 x 4 hours of layover)

Keep in mind that actual duration would vary depending on a number of constraining factors, including the specific available flights, weather conditions, actual speed, and actual time spent waiting for layovers. Also note that I used the actual circumference of the earth for the distance even though the distance would vary based on the routes chosen. This results in a rough ball park figure, not the actual amount for a given flight.

Now, for a specific flight plan:
Start in New York City, USA and fly to London, UK (flight time: approximately 7 hours)
From London, fly to Dubai, UAE (flight time: approximately 7 hours)
From Dubai, fly to Singapore (flight time: approximately 7 hours)
From Singapore, fly to Sydney, Australia (flight time: approximately 8 hours)
From Sydney, fly to Santiago, Chile (flight time: approximately 13 hours)
From Santiago, fly to New York City, USA (flight time: approximately 10 hours)

This example results in 2.1 days (52 hours).

The reason for the discrepancy between my general estimate and the estimate for the given flight plan is that these flights take place in higher latitudes, and thus do not circumnavigate the entire globe. While it is a more realistic route, it technically doesn't satisfy the condition you provided of circumnavigating the entire Earth. Let me take another stab at it that selects routes that are closer to the equator:
Miami (MIA) to Quito (UIO) - Duration: 4 hours 45 minutes
Quito (UIO) to Sao Paulo (GRU) - Duration: 5 hours 35 minutes
Sao Paulo (GRU) to Johannesburg (JNB) - Duration: 8 hours 25 minutes
Johannesburg (JNB) to Colombo (CMB) - Duration: 9 hours 25 minutes
Colombo (CMB) to Singapore (SIN) - Duration: 4 hours 25 minutes
Singapore (SIN) to Darwin (DRW) - Duration: 4 hours 40 minutes
Darwin (DRW) to Dili (DIL) - Duration: 1 hour 25 minutes
Dili (DIL) to Jakarta (CGK) - Duration: 2 hours 25 minutes
Jakarta (CGK) to Chennai (MAA) - Duration: 5 hours 5 minutes
Chennai (MAA) to Muscat (MCT) - Duration: 4 hours 30 minutes
Muscat (MCT) to Cairo (CAI) - Duration: 4 hours 40 minutes
Cairo (CAI) to Casablanca (CMN) - Duration: 6 hours 35 minutes
Casablanca (CMN) to Miami (MIA) - Duration: 9 hours 5 minutes

This plan would take about 60 hours and 40 minutes which is much closer to my estimate.