There is a lot of interest in digital "fingerprinting" for mobile devices. Given some recent moves from Apple: http://techcrunch.com/2014/02/07/openidfa-a-solution-to-idfa-related-app-store-rejections-debuts/ there is some increased interest.
One can do this by combining features that make the device somewhat unique. This fingerprint does not need to be totally unique or 100% stable, just unique and stable enough to match a click to an app launch within a small period (say 1 week).
Here is a closed source version: https://github.com/ylechelle/OpenIDFA
And an open source one (from me): https://github.com/mcorner/ActuallyOpenIDFA/
There are a number of features used here: https://github.com/mcorner/ActuallyOpenIDFA/blob/master/aoi/aoi.m
Some obvious features are not usable without user permission (location, contacts) and therefore can't be used with advertising. Others are not usable across apps (like the vendorID), thus aren't usable from connecting a click in one app to a launch of another. Others are not particularly stable (like IP).
What other features of iOS might be useable?