Once you have decided where you want to go and what you want to do you will need to check out the legal considerations. EU nationals can legally work in any other EU country without the need for a visa.
Countries such as the USA will only offer visas to individuals with evidence of a definite job. In this case, the visa application is instigated by the employer. It may be possible to work on a short term basis without a visa if, for example, your company had offices in the USA. This would only be a short term measure and would not be a permanent arrangement.
Many countries such as Australia and New Zealand offer working holiday visas for those who wish to combine work and travel for periods up to a year, for example, students on a gap year.
You can find current information on visa applications, working regulations and whether it is safe to travel to your destination on the Foreign and Commonwealth Office website.