BBC Worldwide has established an agreement with video site Blinkbox. The deal means archived BBC shows, including Gavin & Stacey, will soon be available via the site.
Unfortunately, they appear to charge £1.89 per episode and are for UK-audiences only.
You can always purchase the full-series of Gavin & Stacey from the James Corden Fan Store at Amazon. UK users can also use the handy carousel below.