Now, now...
...let's not scare Caesar away!
To answer one question: "euphonic" literally means "good sounding" (the roots are Greek). In the context of audio equipment it means that the sound has been "tailored" to deviate from the technical ideal of flat frequency response and low distortion to "sound good". Note the use of quotes. Some people like a bit of rolloff in the high end or a bit of second harmonic distorion. In the case of high-end CD players (Wadia, for one example), often the former method is used to remove the alleged "harshness" or "edge" from CD's. This is generally done in the DAC stage. Some high-end CDPs even use tubes in their DAC output stages, which may also introduce some "euphonic" distortion! Many audiophiles like this effect without knowing the simple manner in which it is achieved, and the high-end marketers disguise it with airy prose. In effect, the player has built in EQ. So, such players will indeed sound "different" even in blind tests. Whether this difference is desirable is another matter. IMHO, that's what tone controls (however unfashionable they may be to the high-end) and equalizers are for.
WmAx and mtrycrafts, however, um, insistent they may sometimes seem, are basically right. Modern CDPs (indeed, all properly designed purely electronic audio components) are basically transparent, having flat frequency response and distortion below the threshold of human hearing, so unless they are purposely "euphonic" as above they'll sound the same in controlled listening tests, regardless of the sophistication, training, or hearing acuity of the listeners. "Properly designed" means simply that the units are level-matched to within 0.1dB (because small differences in loudness can be perceived and mistaken for quality differences), and the identities of the units are disguised from both the subjects and experimenter ("double-blind") to remove bias. Oh, and with CDPs you do have to synchronize them as pointed out above. However, a test with the same short passage played completely first on one, then the other might also have some validity for an informal test if synchronization isn't possible and if the delay between samples is short. But you can't fudge the level matching.
Also note that in a properly designed ABX test the subjects aren't asked to choose the "better" unit or make any qualitative judgement. They are only asked if the two sound the same or different.
The claim that distortion is cumulative is correct but is erroneously simplistic. The typically much greater distortion of speakers will mask a great deal of upstream distortion before it becomes noticable. On my "wisdom" page (see link in my sig) there is a link to a site with distortion samples you can play. If you listen, as I did, to the even-order ("good sounding") distortion samples thru typical mediocre PC accessory speakers you'll be amazed (or appalled?) at how much it takes before becoming noticeable!
Bottom line: high-end CDPs and other high end electronics can be nice to have for reasons other than sound -- like build quality, cosmetics, features -- but a Discman and a top of the line [insert brand here] will sound the same jacked in to the back of your receiver unless the high-end unit is purposely designed to introduce "good sounding" frequency response errors or distortion. If you seek better sound, the room and speakers are the first things to consider as said earlier.
Maybe -- just maybe -- there is a teeny tiny audible difference between some of the lowest- and highest- end DACs these days. But it's doubtful at best (I'm not losing sleep over it!). But direct digital links are indisputably equal. And jitter is a non-issue. The consumer audio press (especially Bob Harley of Stereophile) has made a mountain of that particular molehill.
The diminishing returns point is up to you!
