iTunes Connect Screenshots Sizes for all iOS (iPhone/iPad/Apple Watch) devices

Question

The following resolutions are acceptable to iTunes connect:

• iPhone 3+4 (3.5 Inch)
  • 640 x 960
• iPhone 5, iPhone 5S, iPhone 5C (4 Inch)
  • 640 x 1136
• iPhone 6, iPhone 6S, iPhone 7, iPhone 8 (4.7 Inch)
  • 750 x 1334
• iPhone 6 Plus, iPhone 6S Plus, iPhone 7 Plus, iPhone 8 Plus (5.5 Inch)
  • 1242 x 2208
  • You need the screenshot in this resolution, the phone scales them down to 1080 x 1920
• iPhone X (5.8 Inch)
  • 1125 x 2436
• iPhone XR (6.1 Inch)
  • 828 x 1792
• iPhone XS (5.8 Inch)
  • 1125 x 2436
• iPhone XS Max (6.5 Inch)
  • 1242 x 2688
• iPad Mini 2, iPad Mini 3, iPad Mini 4 (7.9 Inch)
  • 1536 x 2048
• iPad 3, iPad 4, iPad Pro, iPad Air, iPad Air 2 (9.7 Inch)
  • 1536 x 2048
• iPad Pro (10.5 Inch)
  • 1668 x 2224
• iPad Pro (12.9 Inch)
  • 2048 x 2732
• Apple Watch Series 1, Apple Watch Series 2, Apple Watch Series 3 - 38mm (1.5 Inch)
  • 272 x 340
• Apple Watch Series 4 - 40mm (1.57 Inch)
  • 394 x 324
• Apple Watch Series 1, Apple Watch Series 2, Apple Watch Series 3 - 42mm (1.65 Inch)
  • 312 x 390
• Apple Watch Series 4 - 44mm (1.78 Inch)
  • 448 x 368

Hope this helps. Even Apple's Documentation on the matter is incomplete.

Update: Apple has introduced a new Media Manager which requires only that you create artwork for the largest iPhone and/or iPad devices. The smaller images will be created for you. Note that if you hadn't been creating iPad Pro images before, you have to now (if you support iPad).

Update: Screenshots and app previews for new devices now supported.

This answer is updated for Xcode 11.

App Store Connect currently asks for images in the following categories:

iPhone 6.5" Display

This is 1242 x 2688 pixels. You can create this size image using the iPhone 11 Pro Max simulator.

iPhone 5.5" Display

This is 1242 x 2208 pixels. You can create this size image using the iPhone 8 Plus simulator.

iPad Pro (3rd gen) 12.9" Display

That is 2048 x 2732 pixels. You can create this size image using the iPad Pro (12.9-inch) (3rd generation) simulator.

iPad Pro (2nd gen) 12.9" Display

That is 2048 x 2732 pixels. This is the exact same size as the iPad Pro (12.9-inch) (3rd generation), so most people can use the same screenshots here. But see this.

Notes

• Use File > New Screen Shot (Command+S) in the simulator to save a screenshot to the desktop. On a real device press Sleep/Wake+Home on the iPhone/iPad (images available in Photo app)
• The pixel dimensions above are the full screen portrait orientation sizes. You shouldn't include the status bar, so you can either paste background color over the status bar text and icons or crop them out and scale the image back up.
• See this link for more details.

To get screenshots of the proper size without having to create them manually -- run your app in the latest version of Xcode and choose the iPhone you need screenshots for, then hit cmd-s while viewing the simulator. This will save a screenshot to your desktop in the full resolution that you need for submission.

As noted below by @HoffZ, be sure that the scale is set to 100%.

In Xcode select simulator you want:

In the Simulator menu set the scale to 100%:

Press cmd-s to save:

In Xcode 9, in addition to setting the Window Scale to 100% (⌘1) it is now necessary to also uncheck Optimize Rendering for Window Scale in the debug menu in order to get a screenshot of the proper resolution.

To take a screenshot of the proper size for use on the app store:

1.) Run app in simulator
2.) Set scale (⌘1)
3.) Uncheck Optimize Rendering for Window Scalein debug menu
4.) Take a Screenshot with ⌘S