I just wanted to list here all the things I have done to resolve this issue since it has happened to me a few times, with different reasons each time.
Release then Debug
Sometimes you need to run it in Release mode first to the emulator, then you can switch back to Debug mode and it works.
Fast Deployment
Go to the properties in your Android Project
Go to Android Options
Turn off Fast Deployment
If that doesn't work, you can also try
Turning off Shared Runtime
Settings the Linker to Don't Link
Check your logs
Open up the Android Device Logging, connect to your emulator and see what messages are coming back.
For me I saw an Out of Memory Exception. The emulator only had 323 MB of memory set for it. Open the emulator manager (the icon next to the device logging) and then edit your emulator. Increase the memory to 512 MB (that did it for me), and it all started working again.
If this doesn't resolve your error, more scenarios are updated at Debugging Xamarin Android Build and Deployment Errors.
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