Iyoten: This is the first app I've ever recommended. It's a great lockscreen replacement that gives you quick access to your notifications, camera, and it gives you a set of 5 apps (with an expandable drawer of 5 more) that it predicts that you'll need at the time - and it actually seems to work! In addition to those 10 apps, you can pin 10 more apps to be always accessible. It has a bit of lag and it's still in Beta, but it's awesome and worth checking out.
Snapdragon™ Glance is an intelligent lock screen application, which makes it easy for you to quickly access the information you need.
At a glance you can quickly see what is new since you last looked at your device: view important notifications, see when your next appointment is, check the weather, launch relevant apps and contact people more quickly.
Once installed Snapdragon Glance launches each time you turn your screen on. From here you can use Glance or select the Home or Back buttons to access your regular home screen. Requires Android 4.3 or later.
If you experience problems using Snapdragon Glance, we'd really appreciate if you would send us an email to firstname.lastname@example.org explaining your problem prior to leaving a review – we’ll try to respond as soon as possible. We have lots of exciting new features planned for the future so we’d love to get your feedback as well.
Make phone calls, read call log, read contacts: quickly call or text your contacts
Messages: show number of unread SMS messages
Read calendar: show next calendar event
Location (approximate): retrieve local weather information