Can't run Android Studio on Yosemite
Can't install Java 7 (installer refuses).
Can install Java 8.
But then starting Android Studio, it says it needs to install the legacy JDK 6, which is not going to work for me because our projects are already 1.7.
We now have an official page describing what to do: http://tools.android.com/tech-docs/configuration/osx-jdk
Please, please don't edit Info.plist; that has many downsides (including broken patches and application signatures breaking etc). As of Android Studio 1.0 we have a different way of setting the JDK to be used by the IDE.
This should be the final update on this question.
After the final release of Android Studio v1.0, there is an official way to select your JVM, mentioned here:
All the following information is kept only as reference, please don't use it.
Editing the Info.plist file as suggested in this answer might break your IDE. Please check out the prescribed solution mentioned by the IntelliJ folks, and this is the prefered fix to this problem.
If any of the misbehavior/undesired effects mentioned there happen with your setup by using this fix, you should restore the plist file, and use the legacy JDK 6 instead.
If JDK 6 is not an option for your setup, or still have some difficulty to start up the IDE, you can try this fix at your own risk.
Please also read the comments under this answer to review feedbacks from other community members(yes, good and bad) and my discussions with them.
This is an outdated answer, when Yosemite is in early Beta stage and could mess your current setup(see the comments, mostly caused by incompatible JVMs when you do need to update/upgrade them).
As mentioned in the original answer, this is a "dirty" fix that time, and the most suitable way to fix this problem now is to upgrade/update your JVMs as suggested for your OSX system.
Original answer is put below just for reference, if all the JVM upgrade/update still doesn't work for you, at least you can manually install a JVM and use this hack, but please don't upvote this answer because there are better ones.
As mentioned as other users, the JDK from Apple and new OSX seems mess things up.
However, there is a dirty quick fix for it.
First, locate your Android Studio, for my machine, it is here:
jerry-retina-mbp:Android Studio.app jerry$ pwd /Applications/Android Studio.app
Then find the application bundle description file for it, named "Info.plist":
jerry-retina-mbp:Android Studio.app jerry$ ls Contents/Info.plist Contents/Info.plist
Use "Finder" to open this folder:
jerry-retina-mbp:Android Studio.app jerry$ open Contents
Then, you can use whatever text editor you like, to modify the JVM settings in "Info.plist"(which is just a XML file).
Hopefully after this change, your Android Studio will not complain the JVM again.
If you click "more..." on error dialog it will lead to Java for OS X 2014-001. Just download and install it.