If you have a biological or adoptive grandparent who was born in the UK (England, Northern Ireland, Scotland or Wales), you have rights to the UK Ancestry visa.
This means that you are entitled to immigrate to the UK and live and work there without any restrictions. You are also entitled to bring your spouse and children along with you.
The UK Ancestry visa is valid initially for 5 years where the majority of those 5 years must be spent living in the UK. This is if you are intending on remaining in the UK forever. You have to spend at least 9 out of 12 months in the UK and have proof thereof in order to eventually apply for your British passport and citizenship. Once you have lived out your 5 years, you can then apply for your ILR (Indefinite Leave to Remain). This is valid for 1 year after which you may be able to apply for your permanent residency. It is important to note that residency will only be granted to those who can provide evidence that they are a working and active citizen in the UK I.e: you have a job, house, car etc.
The basis of the UK Ancestry visa application is proving your genuine blood or adoptive ties to the UK born grandparent. There is a requirement for various birth and marriage certificates to be produced so this application may take some time if those certificates are not readily available. So be prepared, but it will be well worth the wait!
For those who have parents born in the UK, you have the right to apply for your British passport right away!!!
Other ways to enter the UK include the Tier 1 Visa, which has replaced the Highly Skilled Migrant Program, Family type visas (for children, spouses and fiances of British passport holders) and the UK Travel visa, which are only for those who wish to travel to the UK temporarily for business or leisure.