I've only had these headphones for a few days, so these can be considered preliminary impressions.
 
Using Spotify Extreme with Equalify plugin -> Schiit Bifrost Multibit -> Violectric V200 -> HD800 S
 
Build quality seems as good as I would expect from Sennheiser for the price.  Comfort is very good, though the fit isn't quite as good as HD600.
 
I'd rather see them make the balanced cable optional if that would lower the price a bit.
 
Without EQ, I find the bass and upper mids both to be just a little lacking and prefer the sound I get from my HE-560.  
 
With EQ, the HD800 S sound is the best I have heard to date.  Brings together the best aspects of my HE-560 and HD600 while improving on soundstage and imaging.
 
Here are the EQ settings I'm using at the moment:
 

 
Bottom line for now: Top notch build, comfort, and sound.  Well worth the price IMO.

At the time of this writing, these headphones cost less than $100 on Amazon.  At that price point, they are an incredible value.  For some reason, these headphones seem to be damned with faint praise in many reviews on the web. 

What the 558 offer:
-Beautiful, natural, relatively neutral sound overall
-Forward, engaging mids (what I like best about these)
-Non-fatiguing highs
-Rich bass with good bass impact but not exagerrated bass (look elsewhere for "bass monsters")
-Wide soundstage
-One-sided, replaceable cable
-Good looks 
-Easy to drive (50 ohm impedance means you can drive these easily with iPod, phone, etc)
-Supremely comfortable on my fat head

What they don't offer (and neither did the HD600):
-Great sub-bass extension

Other points to consider
-As an open design, these do not offer noise blocking or prevent leakage (this is not a con, per se)
-They come with a 10ft (really long) straight cord terminating in a 6.35 mm stereo plug. The 3.5mm adapter is a bit unwieldy for use with phones, etc. However, Sennheiser offers a separately sold inexpensive 4.5ft replacement cable with a 3.5mm termination, perfect for such uses

If you are not using a dedicated amp and are looking to plug headphones directly into your phone/MP3 player/laptop/computer, don't need closed headphones to keep sound out/in, then IMO these are the best Sennheisers available and one of the best choices of any brand at any price point.  
 
The only limitation I find is that the bass extension is not adequate for 2% of my rap and electronic music.  Eg, ODB's "Harlem World" or MF Doom's "Hey".  Otherwise they sound fantastic with all genres (including rock, jazz, pop, and 98% of my rap/electronic).

I have the DT-880 Pro (250 Ohm) model and also own and regularly listen to a Hifiman HE-400, Sennheiser HD600, Beyerdynamic DT770 Pro (80 Ohm), V-MODA M-80, and others.

The DT-880 is really the only one that I find to excel at all genres from rap to classical and everything in between. None of the others have this much bass extension and impact, detailed highs that sparkle (a little bit sibilant though), and an overall neutral sound signature. For that reason, and because they are lighter and more comfortable than the HE-400, the DT880 are my most-used headphones.

Compared to the Sennheiser HD600, the DT880:
-Have better sub-bass extension
-Are more detailed
-Have cord on only one side (more convenient but less reliable over time)
-Have fixed cord (cannot be replaced)
-Have a wider soundstage
-Are less natural sounding
-Are more sibilant/fatiguing. Cymbals sometimes sound harsh.

A few words for those trying to pick between the DT-880 models:

-The Pro and Premium 250 Ohm use the same drivers and therefore sound exactly the same except that the clamp strength is slightly tighter for the Pro than the Premium, which changes the sound a tiny bit (more bass). If you stretch the headband a bit on the Pro, it sounds exactly like the Premium

-The 32 ohm model is meant to be driven by phones, iPods, etc, does not need a dedicated amp, but many who have compared it to the others say that it does not sound as good as the 250 and 600 ohm models

-Most who have done side by side comparisons of the 250 and 600 ohm models find that they sound the same, yet the 600 ohm model has a reputation for being the best sounding, likely because the people using it are pairing it with higher end amps, or possibly just because of "placebo effect". I would and did get the 250 ohm model because it is easier to drive (I can use them without a dedicated amp if I need to, though they sound much better if I do.

-The Pro model comes with a coiled cord, while the Premiums have a straight cord. They also have obvious style differences. I preferred the coiled cord and looks of the Pro model.

The current sub-$200 price of the DT-880 Pro 250 ohm model on Amazon is a steal. They are absolutely at the quality and performance level of my $400 Sennheiser and $300 Hifiman.

I've got 3 pairs of these - two came with iPhones (mic version) and one with an iPod Touch (no mic version).  All sound the same.
 
The EarPods sound much better than I expected they would, and despite owning many more expensive headphones, these have a regular place in my rotation.
 
Sound is natural and nicely balanced - very pleasing signature.
 
For the most part, I use them in the office, where I want to be able to listen to music but also to hear others around me.  My other headphones are either too big and bulky or too isolating.
 
The only downside for me is that they slip out easily, and falling out halfway on one side leads to very imbalanced audio.  This is the flip side of their superb comfort and fit.

First things first, there is a simple trick that solves all the complaints about the cable connectors - simply rotate each 720 degrees counterclockwise to build up some torque before you screw each one on clockwise.  Since you only need to screw 540 degrees clockwise to fasten them, the extra twist remaining in the cable keeps them securely fastened without having to overtighten.
 
The build is nothing special.  Yes the R/L markings rub off.  Also the screw placement is oddly asymmetrical.  Materials are not luxurious, and comfort is just average (though comfortable enough that I can enjoy them for hours on end without distraction).  They are somewhat heavy.
 
Bass is incredible.  In this price range, I am unaware of any headphones with this kind of bass extension, impact, and natural sound.
 
High mids are a bit recessed (less so with the velour pads), yet the mids as a whole remain clear, detailed, and vocals show great depth.
 
Speed, transparency, imaging: all strong suits.
 
These headphones absolutely shine with jazz, rap, electronic, funk, rock, and pop.