They're all over the place for core functions - whenever you click a "Share" button it will ask which applications can handle the content you want to share and add them to the menu. I've also been prompted to choose whether I want to make phone calls using the built in dialer or Skype, which I presume is using intents as well.
Where I've not see so much use is providing completely new intents, presumably because its so hard to get any sort of agreement on how they should be implemented.
BlackBerry has this also. I can share anything with any app that I have installed (and that can support sharing of some sort). I don't know how this is implemented or if it is even the same principal as this behind the scenes...
Whilst that might be cool technology, I wonder at the user experience and confusion when my mum clicks on the phone icon and all of a sudden this menu appears asking me whether I want to use the phone or skype (obviously I get that the call can be done with either, but mum probably doesn't).
If your mother doesn't have skype installed she wouldn't get this message. If she does, I would presume she knows what skype is for.
Additionally for the big system-level intents there is an "always use this action" which is useful so you don't have to repeatedly tell it to use the phone app to place phone calls.
The iPhone experience is that the system Contacts app is only for calling via the phone system. If you want to call via Skype, you open Skype and then use its embedding of the system address book. It is really quite clunky.
Where I've not see so much use is providing completely new intents, presumably because its so hard to get any sort of agreement on how they should be implemented.