Places like NZ and Oz you dont need a visa if you are just visiting but if you plan to work here you need one. NZ does a working holiday visa and I presume a few other places do the same. It usually costs a bit to apply for them (i think my student visa cost around $80 but that may have gone up recently). With the working holiday visas you are usually allowed to work in one job for a max of 3 months before you move on and find another one and there are quite strict rules about what you can and can't do.
The other option is to come to places like NZ as a visitor and do 'casual' work (technically illegal but heaps of people do it). Alot of travellers in NZ do fruit picking and similar things as its just cash in hand. To come in as a visitor you will need proof that you intend to leave again i.e. a plane ticket back out or prove that you have enough money in your bank account to live on and pay for a plane ticket out, but it varies from country to country. I think you can stay between 3 and 6 months as a UK visitor with no visa in NZ.
Thats just for NZ, i know when i went to Bolivia i didnt need a visa to get in but i probably would have needed one to work. Like DBB said its defo best to work that stuff out before you leave, especially in terms of money as you may underestimate how much its going to cost.
And depressing as it is i'm with DBB on the hitchhiking. Even in awsome countries like NZ its just not safe anymore but theres heaps of good transport networks for travellers in NZ and Oz if you plan on coming here
Enjoy, i'm very jealous!