If you are thinking about moving abroad, the question isn't really "where would you like to go?" but "which countries might allow you to immigrate".
If you are an EU citizen, you probably already know that you can
move to any of the other countries, similarly if you are an Australian or NZ citizen you can move to the other country under the
Trans-Tasman agreement, and if you are a British or Irish citizen you can swap countries through the
Common Travel Area.
But what are some of the other options?
Irish citizenship β can live and work in the European Union, Switzerland and in the UK
If you have a parent or grandparent who was born on the island of Ireland before 2005, you may be able to gain Irish citizenship. If your claim is through a parent, then you are a citizen and can apply for a passport. If your claim is through a grandparent, you need to apply to the registry of foreign births to get Irish citizenship first. The registry of foreign births is currently taking around 9 months to process applications but is otherwise relatively straightforward.
Italian, Spanish or Portuguese citizenship β can live and work in the European Union and Switzerland
If you have a parent or grandparent who was an Italian, Spanish or Portuguese citizen, you may be able to gain Italian, Spanish or Portuguese citizenship respectively. This can be a reasonably time-consuming route in relation to the supporting documents and may benefit legal assistance.
Italian law changed earlier this year; it used to be much more generous in relation to how far back your Italian ancestor could be. Spanish law is changing later this year.
German citizenship β can live and work in the European Union and Switzerland
If you are the descendant of a person who lost their German citizenship due to Nazi persecution, you may be able to (re-)naturalise as a German citizen. You will need to gather documents to prove that the 'reference person' was a German citizen, that they lost their citizenship in one of four ways between 30 January 1933 and 8 May 1945, and that you are their descendent.
Finding out what happened to your relatives in the Holocaust can be more traumatic than people expect, and not everyone who begins the process chooses to gain German citizenship.
Digital nomad visa β live and work in the country that issued the visa
Estonia, Portugal, Thailand, ,...
If you are a remote worker, you may be able to get a digital nomad visa for an increasing list of countries. This will allow you to live for an extended period of time while earning an income from remote work carried out for a foreign company. Details vary between countries.
Skilled immigration visa β can live and work in the country that issued the visa
Australia, Austria, Canada, Germany, Ireland, New Zealand, Norway, UK,...
People with the right skills and experience may be able to apply for a visa that allows them to live in the issuing country without having a job offer. The length of the visa varies significantly depending on the country β Germany offers a 6-month job seeker visa, while Canada offers some immigrants immediate permanent residency. These countries typically have a route to citizenship although this may take up to 10 years.
NAFTA/CUSMA visa β can live and work in the USA, Canada or Mexico
If you are a Canadian, Mexican or US citizen whose occupation is on the relevant list, you can apply for a visa allowing you to live and work in one of the other two countries for three years. In theory this is renewable indefinitely, although it is at the discretion of the authorities. There is a similar provision
UK ancestry visa β live and work in the UK, with a route to citizenship
If you have Commonwealth citizenship, and one of your grandparents was born in the UK, you may be able to apply for a UK ancestry visa. This gives you the right to live and work in the UK for 5 years and can be renewed indefinitely. After 5 years of continuous residence in the UK, you can apply for British citizenship which also allows you to live and work in Ireland.
Student visa β study in the country that issued the visa with a route to a work permit
Australia, Canada, Ireland, New Zealand, the UK, many European countries
Study for a degree in a foreign country and they may allow you to stay once you have graduated to look for work. There is usually a time limit on how long you can stay before you need to switch to a different type of visa. The time limit is typically somewhere between 6 months and 2 years. Will need to demonstrate proficiency in the language of the relevant country.
Work visa with a job offer β work in a specific job in the country that issued the visa
More or less everywhere
In most countries it is possible to get a work visa if you have a job offer. Often, your prospective employer must be able to show that there was no one suitably qualified for the job in the country.
Working holidaymaker visas β live and work temporarily in the country that issued the visa
Australia, Canada, New Zealand, Japan,...
If you are young (under 30 or possibly 35) you may be able to apply for a working holidaymaker visa. The most popular destination might be Australia where citizens from a long list of eligible countries are able to get a 1- or 2-year visa. Depending on the specifics of the programme, there may or may not be an opportunity to transition to a longer-term visa. Probably best thought of as a temporary option.