There is no all-around answer to this. It depends crucially on the standard of living you require, the length of the trip and number of places you want to visit. Almost anyone living in the rich parts of the world could do some kind of around the world trip. The cheapest way that comes to our mind is just flying around the world quickly.
When we got to Delhi we were considering whether to visit Taj Mahal or not. It would mean a two-day trip to Agra (you can do it in one day from, but then the place might get crowded and you miss the sunrise) and Risto was quite sick. However, his condition was getting better, and we decided to book a flight to Goa on 18th, so a two-day trip to Agra got possible. And many of those train station scammers told us that visiting Taj Mahal is a must, so why shouldn't we believe them.
The flight from Dubai to Delhi went surprisingly well, taking Risto’s condition into account. The combination of painkillers and antibiotics must have done their job. We sat next to a young man from North India who had been working in Dubai for two years, and now got to go home and see his son. He was so excited that the joy got into us as well.