+1 on the Fiio E7. From what everyone says, the Shure monitoring line really needs the extra power to sound good. In fact, I remembering demoing a pair at a Guitar Center, and I'm wondering now if they had it hooked up to an amplifier or not... because I wasn't too impressed... but maybe I needed more time to adjust. E7 is good for headphones that aren't power-hungry. Not sure about the Shure monitoring line or how demanding they are. If it isn't enough, the E7 + E9 combo has a lot of power.
Not advised. Shure headphones are ugly, imo. The headbands are really ocward looking, and while I'm unsure about Shure's monitoring line, I have the 750Dj's and I find turning up the volume a little too high in places with a lot of background noise. I can assume the 940's would look even stranger, considering their design. Also, Shure's monitoring line require an amplifier for use, as they don't sound good at all without one. This might put you back a bit in money and portability.
Nope - they don't need an amp. Out of my iPod Touch's headphone out - they still sound great. The reason I use an amp with them is because 'to my ears' I get additional clarity and separation. It's not night and day. I'd estimate it maybe contributes an extra 5-10% to my enjoyment of them. The extra clarity / detail is worth it to me - especially at the bargain price of the E7. I'm interested to see if the E11 gives the same or better (once it arrives this week).
Saying they (SRH840) do not sound good without an amp is IMO a misrepresentation. Can't comment on the 940's or 750DJ's though.
And they don't need a great deal of power either. Using my current set-up : Touch G4 > LOD > E7 > SRH840, I'm only at about 20/60 on the E7 - and that is pretty loud. So the E7 for me is a good match by itself. Using FLAC ripped myself from CD's.
The 'ugliness' factor is a personal one. FWIW I'd have no issue wearing the 840 or the 940 in public (it'd be worth it for the SQ). I wouldn't be seen dead with the Beats though. IMO they are ugly. A lot of people think differently. I guess I'm not as fashionable as I once was ;) Moot point though - for out and about in public, if you can wear them, I'd always recommend a decent IEM first.