(1) You can completely replace the operating system and various components with ease. Jailbreaking = the most difficult and tedious thing I've ever seen, and I don't consider myself to be technologically incompetent

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(2) Stock, you can do a bit more and customize it plenty with the use of widgets, launchers, toggles, etc. That type of customization is only available while being jailbroken, but again, see #1 for my thoughts on that.
(3) Sort of like #1, the ability to replace and customize various file system pieces and phone system images is incredibly powerful if you (a) know what you're doing, and (b) adequate development/support is available. For example, changing the kernel adds so much more "power" and "flexibility" that kernel replacement alone makes Android a more powerful and adaptable base system--IMO.
(4) Aside from "hacking," you have, generally, 4 major Android "flavors." You have stock (Nexus), TouchWiz (Samsung, HTC (Sense), and Motorola (Motoblur). While some point to this as a weakness, many consumers appreciate being able to have the same "ecosystem" while having the ability to choose hardware/software that best reflects their needs, desires, etc.
There's plenty more, but those are the big 4.