If you use google's email/calendar/etc then the mobile sites of these things are actually very nice. It does require you to be connected to wifi to use them but if you are always around a wifi network I have found them to be a better option than the included email program. Just go to your browser and visit
https://google.com/mail or
https://m.google.com
Also the mobile version of Google Music looks pretty much just like the android app. Once again though you won't be able to pin playlists and store them locally so only good if you are on wifi.
If you visit these sites, bookmark them, then go back to your homescreen they will be on the Carousel and you can then add it to your favorites. This should be true of any site you want to put in your favorites. Now if I could just find a way to change the icon for bookmarks favorited.