Is there a way to see Minecraft's source code?

JAR files are simply ZIP files, so you should be able to open them with the archiving tool of your choice. Even Windows Explorer will open them if you change the file extension to .zip.

However, looking at the source isn't as easy as just unpacking the archive. It only contains the compiled .class files, and even if you do get your hands on a JVM byte code decompiler, it's obfuscated and spread out over hundreds of files.

You might want to have a look at MCP (Mod Coder Pack, formerly Minecraft Coder Pack), though. It's a community project that decompiles and (mostly) de-obfuscates the Minecraft sources to aid modders.

There's a way to do this; in fact, this way as well allows you to edit the code and... make your own mods! It's called MCP (Minecraft Coders' Pack), and is a bit of a complicated setup, but it is how nearly all Minecraft mods are made. Check out a video I made on YouTube on setting up and installing it:

Interestingly enough, mention of source code release comes straight from the minecraft website.

"Once sales start dying and a minimum time has passed, I will release the game source code as some kind of open source. I'm not very happy with the draconian nature of (L)GPL, nor do I believe the other licenses have much merit other than to boost the egos of the original authors, so I might just possibly release it all as public domain."