Who is entitled
Entitlement to the personal allowance and blind person's allowance is dealt with in Income Tax Act 2007, Part 3 Chapter 2. Tax reductions for married couples and civil partners are dealt with under Chapter 3.
Chapter 4 then states that the above allowances or tax reduction may be claimed for a tax year where the individual is resident for the tax year.
Even if an individual is not resident in the UK they may be able to claim personal allowances if they meet certain criteria. Please see here.
UK resident but non-UK domiciled individuals who claim the 'remittance' basis for a tax year are not entitled to the personal allowance or blind person's allowance (S809G ITA 2007). See below comments however for dual residents.
If an individual is 'dual resident' in the UK and in one of certain other listed countries, then he/she will be able to receive UK personal allowances in any tax year the remittance basis is claimed. (For more information, see the Residence, Domicile and Remittance Basis Manual page on the HMRC website.
At Budget 2014, the government launched a consultation on whether or not to restrict the income tax personal allowance for non-residents. Although the government is keen, it recognises the complexity for both employers and individuals who may be affected. Accordingly, the government announced in Autumn Statement 2014 that it will continue to discuss implementation of this change with stakeholders. Should the government decide to proceed, a more detailed consultation will be undertaken.