SmoothSync for Cloud Contacts syncs your iCloud contacts. Due to its implementation as sync adapter it integrates seamlessly with the native contacts app and operates invisible in the background.
This app is bundled with Contact Editor Pro to allow you to edit synced contacts on pre-Android 4 devices.
Also, check out SmoothSync for Cloud Calendar to sync your iCloud calendars!
Samsung S5 users: Please note that some S5 devices come with a broken contacts app that crashes when opening a contact synced by this app. Please report any crashes to Samsung.
Important note for Android 4.1 and Samsung users: To prevent the removal of your accounts on reboot install this app (before you install SmoothSync):
https://play.google.com/store/apps/details?id=org.dmfs.jb.workaround.icloudcontacts
As of Android 4.2 this issue is fixed and the workaround no longer necessary (except for Samsung devices), please uninstall it....
