Barclays Arrival 40,000 miles (up to $420 & 1st year free)

[Update September 2015] Barclays slightly devaluated its miles from 1.11 cents to 1.05 cents per mile effective August 2015 (for new cardholders) and November 2015 for cardholders who opened the card before October 2014.  We have updated the title of the post.  both landing page and application page are updated as well.  You will need to spend $3,000 within 3 months of new account opening to receive 40,000 miles, which are now worth $420 in travel.

2015 Lading Page
2015 Application Page

[Update February 2014] Barclays slightly changed this offer - now you need to spend $3,000 within 90 days to earn 40,000 miles.  

2014 Landing Page (redirecting to new landing page)
2014 Application Page (expired)

[Original Post April 2013] Barclays has just upped the signup bonus on its Arrival MasterCard (the $89 annual fee version, the 1st year is free) to 40,000 miles after spending $1,000 within 90 days.  Note that these "miles" are not airline miles but just Barclays' own reward points.  The most valuable way to redeem will be statement credits towards travel expense - 1.1 cent per miles, thus 40,000 miles can be valued at $440 at most.

Landing Page (redirecting to new landing page)
Application Page (expired)

Note that the free version of Arrival comes with a signup bonus of 20,000 miles.  At this point, whether the "two-browser" trick will work for these two cards remains unknown.