I've got a new 2013 MacBook Air 13", with Intel HD Graphics 5000, and it came with a Mini DisplayPort to VGA adapter within the box. A mini DisplayPort to DVI adapter is also available from Apple.
An ASUS PB278Q 27" 5ms WQHD (2560 x 1440) only gets 1920×1080 resolution using the VGA adapter. I'm not aware of VGA being limited to 1080p, and this is not advertised at all anywhere on the ordering page.
As per Google search of Apple's quite scattered and incomplete docs on the matter, which, in the end, still don't cover all custom-order options provided immediately on the ordering page for a MacBook Air, both VGA and DVI adapters apparently only support up to 1920×1200 resolutions, with dual-link DVI being required for "resolutions above 1920 x 1200" (what does this even mean, I'm buying a MacBook Air, what's "above 1920×1200"?). http://support.apple.com/kb/ht3382
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Why resolutions of Mini DisplayPort to VGA and DVI adapters is limited to 1920×1200?
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What is the maximum resolution of Mini DisplayPort to Dual-Link DVI adapter as ordered for mid-2013 MacBook Air 13?
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Does Apple's official HDMI adapter, "Belkin Mini DisplayPort to HDMI Adapter", support "resolutions above 1920×1200"? Which ones would that be?
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What resolutions would I get with a third-party miniDP to DP cables or adapters, or miniDP to HDMI?
Best Answer
You can get full resolution with mini DisplayPort to DisplayPort or mini DisplayPort to Dual-link DVI. Dual-link DVI supports up to 2560x1600 pixels resolution. DisplayPort supports that resolution or even higher.
You will not get full resolution with mini DisplayPort to DVI. DVI is limited to 1920x1200 or something similar. You usually won't get full resolution with mini DisplayPort to VGA.
I do not know whether you get full resolution with mini DisplayPort to HDMI. I think it depends upon your graphics card.
Bottom line. I would recommend using mini DisplayPort to DisplayPort.