How do I keep the Recovery HD and EFI partitions from automatically mounting on my MacBook Air?

I've set Finder preferences on my MacBook Air running OS X 10.9.1 to show everything on my desktop:

I've noticed that storage partitions called Recovery HD and EFI appear there:

What are they? Is there a setting I can use to hide them?

I've noticed I can eject them, but they will reappear later, such as when I wake my MacBook Air after sleeping.

Update: I'm using Mountain (which I recommend), and it turns out either the "Mount all unmounted volumes on wake from sleep" setting was on by default, or I didn't remember setting it.

Since I turned it off those partitions have stopped mounting automatically.

Your computer is currently set to mount and show hidden partitions, which is unusual. To get control of this feature, you need to activate the Debug menu in Disk Utility which then gives you the option of viewing and mounting hidden partitions, or indeed, making them hidden again.

1. In Terminal, run the command

   defaults write com.apple.DiskUtility DUDebugMenuEnabled 1
   

2. Launch (or relaunch Disk Utility)

3. In the Debug menu, uncheck Show Every Partition.

They are hidden partitions in OS X. Showing all partitions in Disk Utility also shows the partitions in the list:

…and diskutil list:

1:         EFI EFI          209.7 MB   disk0s1
2:   Apple_HFS Mac SSD      150.0 GB   disk0s2
3:  Apple_Boot Recovery HD  650.0 MB   disk0s3

They are usually not mounted by default and therefore not shown on the desktop regardless of your settings in Finder.

Try resetting your NVRAM (boot with ⌘⌥PR until the second boot chime).