Q:

What are the dimensions of the Passbook pass images?

What are the correct dimensions of the pass images (such as background.png, logo.png) that can be included in the pkpass packages?

A:

I couldn't find this documented anywhere, but after much experimentation here are what I believe the correct dimensions of the images to be. Note that if you only include the @2x retina image, it will be automatically downscaled for regular displays.
icon

29x29 
58x58 (@2x)
Appears in the mail app, and in notifications about the pass, but not on the pass itself
This image is mandatory, the package will not open without it

logo

30x30 to 300x30
60x60 to 600x60 (@2x)

strip

StoreCard - 310 x 123 or 620 x 246 (@2x)
EventTicket - 310 x 84 or 620 x 168 (@2x)
Will be center-cropped if it is too high

thumbnail

up to 80x90
up to 160x180 (@2x)
will be downscaled if too big, will not be upscaled if smaller than the max dimensions. So an 80x80 icon will appear as 80x80.

background

312x398
624x796 (@2x)
This appears blurred behind the pass. 
I'm not 100% sure about these dimensions, its hard to tell because of the blurring, but they seem to work.

footer
Not sure about this one yet, 200x30 seems to work well.

A:

Images dimensions are specified in Passbook Programming Guide: Pass Design and Creation under section Images Fill Their Allotted Space
Edit: Passbook has been renamed Wallet. As such, all the programming guides have too! Wallet Developer Guide: Pass Design and Creation

A:

Latest 2015 specs, according to Apple's Pass Design and Creation:
logo.png

160 x 50

icon.png
See "small icon" in Icon and Image Sizes, though that document does not specifically has a row for "small icon". I guess "Settings icon" fits.
strip.png
On iPhone 6 and 6 Plus:

375 x 98 for event tickets
375 x 144 for gift cards and coupons
375 x 123 in all other cases

On prior hardware:

320 x 84 for event tickets
320 x 110 for other pass styles with a square barcode on devices with 3.5 inch screens
320 x 123 in all other cases

background.png

180 x 220

thumbnail.png

90 x 90

footer.png

286 x 15

Double all sizes for @2x versions, resp. triple for @3x versions.

