Embed a JRE in a Windows executable?

Try to use Avian and ProGuard toolkits. Avian allows to embed lightweight virtual machine in you app. Linux, MacOS, Windows and iOS are supported. And ProGuard allows you to shrink large jar file to prepare to embed.

There's a new tool that does this: Packr
https://github.com/libgdx/packr

Quite a few options around, commercially this is very good:

http://www.excelsior-usa.com/jet.html

There are two key open source options GCJ and VMKit

http://gcc.gnu.org/java/ and http://vmkit.llvm.org/

Other more prolonged paths would include IKVM.NET:

http://www.ikvm.net/

Which is a .NET JVM which can be statically compiled to an EXE