Some widgets that I find useful:
Google Now: A running display of current weather conditions, upcoming appointments, traffic conditions, and other useful information on your homescreen. Incredibly useful and awesome. (Would be nice if it supported SA sports teams though.)
Google Keep: Like sticky notes for your phone. Useful for jotting small pieces of information for short-term storage.
Google Calendar: I always keep this one swipe away from my main home screen. Being able to check my agenda for the day at any time with a single swipe is just incredibly useful.
Hue: A nice weather app I discovered, with an accompanying widget. It's colour-coded, so you can see at a glance whether the day is going to be sunny, cloudy, or rainy.
Eye In The Sky: Another very nice weather app with an accompanying widget. This and Hue are my two favourite weather apps on Android.
The default Android digital clock: Not amazing or anything, but I find it attractive, and it's useful to be able to check the time at a glance.
DashClock: More intended as a lockscreen widget, but it can also be used as a homescreen widget. Kinda like a more advanced version of the default Android digital clock, with some options to change the appearance and a notification API that apps can tap into.
Power Toggles: Kinda like the stock power control widget that comes with Android, but super-customisable, with a great UI, and 100% free with no IAPs. A great choice if your phone doesn't have (or you don't like) settings toggles in the notification tray. Alternatively, you can control primary settings through the notification tray and secondary settings with this. Or whatever. There's a ton of ways you could set this up.
Falcon Pro: Not the original Falcon widget; I consider the widget in Falcon Pro to be much nicer. A really great Twitter widget and app. Unfortunately, due to Twitter's dickishness, this can no longer be installed from the Play Store; it needs to be sideloaded.
Holo Countdown: A very nice, stylish countdown timer that I use to count down the days to important events.
Now Playing: My favourite music app, which also comes with a very stylish widget.
Pocketcasts: My favourite podcasts app. The style of the widget is very similar to Now Playing, so they complement each other nicely if you want to use both of them.
Gmail: If you receive a lot of emails, you might benefit from essentially having your inbox on your homescreen.
Contact (1x1): This is technically a "shortcut" rather than a widget, but whatever. The nice thing about shortcuts like this is that you can put them into folders, so I've created a bunch of folders which essentially contain quick-dial lists for friends, family members, coworkers, etc.
Tapatalk 4 Topics: Again, if forums are really important to you, you might benefit from having this on your homescreen.
Twee: A really great little app that I use to keep track of TV shows I'm watching. It has a homescreen widget that can tell you which shows have new episodes coming out today.
So yeah, those are some nifty widgets I can think of. Since I'm pedantic, all of the widgets on this list fit in well with the "holo" aesthetic of Android, which means that they also fit well with each other.
if you want to
