I have done a 25 months trip (Around the world but mostly in South East Asia) and a 22 months one (Latin America). I spent about 22,000 Euros each which I saved before or between the trips.
I did not have any regular expenses back home, no health insurance, mortgage, storage fees, family. But I also did not have any income either.
I do not travel as cheap as possible. I use public transport, stay in dorms in good hostels (not the cheapest one, no couch surfing), but also in hotel rooms that are one or two levels up from the cheapest in town. I always eat out to taste the local food. Many backpackers cook for themselves to save money.
I don't take taxis, just public transport but mostly I walk, so make sure you can carry your backpack for 10 miles or more.
Many people take night buses or night trains so they don't have to pay for accommodation. I like to see the country I am visiting so don't travel in the dark unless there is absolutely no other option.
I've met many people who spent half their budget on booze and going out. I do that sometimes but not that often. Long term travelling is different from vacation.
When not travelling I try to live cheaply and save the money I make for the next trip. On two occasions I made enough money in 12 months to travel for 24 months afterwards.
I never worked for money. Sometimes I fix computers or networks at hostels, especially removing viruses and get a free night in exchange. This only works if you can convince the owner that an infected computer is actually a problem.
So my point is, it doesn't have to be the absolutely cheapest way to travel. In the end it
all depends on how much money you can save before.