The incoming call screen got a big overhaul in Android 4.0 last year, but it's still not perfect. An incoming call pulls you away from what you might be doing with your phone. Writing an email? Not anymore you're not. Reading a webpage? You can reload that after the phone call. Small Call notifies you of incoming calls in an unobtrusive way while still preserving functionality.
When your phone rings, Small Call will pop up a floating bar at the bottom of your screen. It has answer and ignore buttons on the sides, and a text button in the middle. You can probably sort out what the answer and ignore buttons are all about, but the text button is a nice addition to this app. It replicates a great feature of the stock phone app, allowing you to send text messages to a caller when you dismiss the call. Small Call can also handle text notifications in the same floating bar, but I actually find this more troublesome than the stock behavior. This can be disabled in the settings.
Small Call has plenty of configuration options for the way calls are ignored, text back phrases, and bar position/opacity. Overlaying third-party apps on basic functions sometimes feels flaky on Android, but Small Call seems to work well. Unfortunately, it's not free and there is no trial version. This one is $0.99 in Google Play.