IMHO push notifications (which appear when you need them or when they are most relevant) are almost always better for UX than widgets (which take up space at all times).
I've got a calendar widget and a messaging widget. The calendar is in 'agenda' mode, so it shows me the next two or three things I'm supposed to do, and I can scroll to see more if I want. Almost everything I need from calendaring without loading the whole app. (Sounds like iOS might not allow scrolling, so then you need to use more screen, which is iffy)
For messaging, I've currently got it showing all messages (from one app), in case I dismissed a push and forgot about it. I used to have a widget showing just messages from my spouse, because I had a lot more messaging going on (used for work) and it was easy for things to get lost. Maybe I could be more organized, but that ship has sailed.
Weather seems like a nice option, but I'm ok with being surprised by unexpected weather.
I rather enjoyed the Windows Phone live tiles, where if you went to the home screen it'd show you all the icons, then if you sat there, things would flip and you'd get tidbits from everything. Widgets aren't quite the same.