Android (rooted): Today, the developers behind Cydia and Mobile Substrate announced that Cydia Substrate will be coming to Android. You read that right: Cydia on Android. In fact, Winterboard is already available.
So, what does that actually mean? Well, Cydia Substrate is a platform for modifying a device without actually having the source code. Technically, the Android community has the source for stock Android, but owners of devices from HTC or Samsung have certain elements that are not open source (and, in fact, neither are Google's own apps). Cydia Substrate allows tweakers to customise those elements without flashing entirely new ROMs.
This is accomplished with what are known as "substrate extensions". By itself, Cydia Substrate doesn't actually do anything from the user's perspective -- it's more of a tool for developers. However, it means we may see some new kinds of tweaks for Android, especially ones coming over from iOS -- in fact, the only extension that's available in the Cydia Substrate app itself is Winterboard, the tool that iOS users have been using to customise their devices for a while. More tweaks and tools will likely arrive in the coming months.
Android users will need to root to install Cydia Substrate, which is available on the Play Store. Also, keep in mind that as of right now, this is all experimental. The developers have tested the app on Android versions from 2.3 to 4.2, but there are a lot of devices out there, so your mileage may vary.