Google Apps without rooting
I have got YouTube, Gmail, Currents and Google Maps working in the Kindle Fire HD without rooting. However Google Maps is not able to get the location from Wifi and is not able to sign in using the following process. I was unable to get GTalk (also attached) to work so far. The following process does not use GoogleServicesFramework as was used in the Gingerbread version of Kindle Fire.
I have modded the apps with high resolution 256x256 icons for display in Kindle Fire Carousel using the following guide.
I have used You Tube 3.5.5 modded for HD playback. Alternatively this works with any of the APKs found in the following topic or built for Ice Cream Sandwich.
1. Enable installation of applications from unknown sources in Kindle Fire Settings.
2. Install GoogleLoginService.apk.
4. Install the Google Apps.
5. Start YouTube. Sign In. It will take you to Google Account Manager to create/use existing Google credentials.
6. Same goes for other apps. In case sign in fails for any of the apps (except Maps/GTalk) drag down the Kindle Fire notification bar, click on the notification for "Permission requested....." and assign required permissions.
The files can be downloaded from here
UPDATE: Thanks to alkemist80, installing GoogleServicesFramework.apk, rebooting & installing Talk from the following post, Talk works perfectly fine on Kindle Fire HD, unless it goes into sleep mode.
(If existing apps stop responding at this point, remove and reinstall them)