I'm fairly new at well...everything (except guest-lurking around these parts) so my knowledge of terminology or specific details will likely be lacking. But it's the reason I have questions (on the ATH-M50's)! The goal: I'm looking to replace and upgrade the quality of my desktop set.
 

1. Do these headphones need an amplifer? Will an un-amped setup (desktop or mobile) suffice? 
   
   Desktop: Creative X-Fi Xtrememusic (PCI)
   Mobile: Zune HD, laptop (with integrated sound)
   
   I'll be using these headphones almost exclusively at home (hooked up to a desktop PC) or possibly at work. I don't think I'll use them while on the go, though it is a thought I've entertained a bit. I've also looked around these parts a bit and mentions of amps are made while talking about ATH-M50's.
   
   (I don't currently have an amp as I'm somewhat new at all this high end hardware ... and probably why I'm asking questions). 
    
2. As part of my research, I found a couple threads talking about EQ and frequency graphs and adjusting the EQ accordingly...
   ...what is this/how does this work/should I even care? 

 
I've previously/currently own (from oldest to newest ... which also happens to be cheapest to more expensive ):
 

1. iPod earbuds
2. Sony MDR-XD200 [current - desktop with Creative X-Fi Xtrememusic]
3. Sony MDR-EX7x
4. Shure SE215 [current - mobile with Zune HD] 

 
Not really planning on buying anything else aside from something to replace my current desktop headphones except maybe an amp depending on responses here. Budget is a consideration for me and I can land the ATH-M50 for $119 right now (Sound Professionals) plus additional duties/taxes/shipping/etc.
 
Also, thanks for any responses ahead of time
 
Oh...and I prefer to not blow my ears off in terms of volume. I'd like to be able to listen well into old age
...as for a more specific idea of what I listen to: zts (trance), TRakker (trance), YUI, ASIAN KUNG-FU GENERATION, Angela Aki, Our Lady Peace, Foo Fighters, The Tea Party, Kaskade, Ayaka, Adele, Supercell, Goo Goo Dolls, Armin van Buuren ... various instrumental tracks...etc. (I think that's a good sample set)

None of that is necessary. It might actually be detrimental given how bright they sound already. 

Eh, I might take that back. I sold someone a Total Bithead who felt that it made his sound better. I would not use gain on them though. 

Thanks for the advice audiophoholic! Will take a look into that...though I guess at this point I suppose an amp is not really needed to make these headphones work (like other headphones I've read about)

I had a pair without amping and IMO didn't need one.

I've done some more reading in the timeskip and I'll probably just go without buying anything else. Also thanks for the input MattTCG and again audiopholic