I have learned a LOT by lurking here.  Love the site.  I can't seem to find information on different ohm loads on the same set of headphones(and how that load relates to the amp).  Let me be specific...I am interested in a set of Beyerdynamics dt880's.  They are available in 32, 250, and 600 ohm load versions.  I understand that he 32 ohm version is designed for plugging directly into an ipod, etc with no amplification.  The 250 ohm version is designed for plugging in to larger home stereo components and the 600 ohm version is designed to go through headphone amps(that description is straight from Tim at Beyerdynamics).  Having said all that, are all of these headphone amps I see people talking about rated at 600 ohms??  Or are there different amps with different ohm ratings designed for different headphone ohm ratings??  And furthermore, what happens if you plug a 250 ohm headphone into a 600 ohm amp??  
     All 3 versions of the phones use the same components I assume. I do not care about high volume.  I do, however, want the phones to be pushed correctly so they sound the way the designer intended.  Can anyone shed a little light?
 
Thanks very much in advance.

Different amps are indeed designed with different loads in mind.
Portable amps and headphones designed for portable use tend
to be lower impedance because it is easier to get more current
from batteries than voltage. Desk amps have the luxury of having
lots of both current and voltage available from the wall socket.
Again though, these amps tend to be divided into either current
domain amps or voltage domain amps. Of course this is in a
general sense and there are amps that have enough voltage
and current to drive pretty much any headphone and headphones
that work on a wide variety of amps. I guess the first step is to
decide whether you want a portable set up or a desk set up.
Find headphones that have the sonic signature you enjoy.
Get an amp meant to drive the type of phones you picked.
In the end, it is more important that you enjoy the music that
comes out of them than whether they are high or low impedance.
In the case of the DT880's that you mentioned, it comes down
to do you want to run them in a mobile set up or strictly at
home or work.