My favorites:
For Calendar:
Week View 8
I've tried them all and this one is really good. It is not free, but it's worth it. Great tile and you don't have to keep paying for each little thing like Simple Calendar, plus it show "private events" unlike Simple Calendar. I liked Chronos but their their month view was kind of lame.
For weather:
Bright Weather
I've also tried them all and I don't really love any of them. However, this one is made by the Beautiful Widgets people and I trust that they will continue to develop this and so far they use accuweather and support many cities. If you need radar, this one won't be for you.
Misc:
ConnectivityShortcuts
Lots of apps do this but this one lets you change the colors of each shortcut so you can easily see which one is bluetooth or wireless etc.
GPS
Copilot GPS
I've tried a few but I really like this one. It is more accurate than Nokia and for me and if you live with Traffic, this one is the one to get. There is a traffic bar on the right that let's you see how traffic stacks up for the rest of your ride. It's visual and accurate. It is another paid app but one id gets you a license on all your devices. I have it on an old android and also licensed on my wife's iphone.
Music
Swipe Tunes
I have the hardest time shuffling my huge collection. Nokia Music refuses to shuffle my 6,000 song collection. All the programs seem to hang while trying to play all the songs and swipe tunes is capable of suffling the entire thing even though it also hangs. Is this a problem with the OS or the 521?
Lockscreen
Today
I've used lots of things, currently using Today, bing image of the day and cute looking weather.
News
News 360
Tried many things. Seems to be the only news app that syncs across all devices.
Home Screen
Group Tiles
It creates headers to better organize my home screen.