Good music soundcard

I have several requirements.

1) Genuine multi-bit DACs and ADC, and not bitstream garbage

2) Ability to switch between 44.1,48,88.2, and 96 kHz without resampling or with a specification showing they can resample very well. Example: Soundblaster cards do not resample well. They also need to be able to resample 176.4 kHz well. I have a DVD-A that uses that sampling rate.

3) Two stereo outputs, one I can use for active monitors and another I can plug into a headphone amp and leave them both plugged in all the time.

4) No gaming support!

5) ASIO 2.0 and EWDM drivers.
The most highly regarded sound cards in the under $200 price range would have to be the e-mu 0404 and the e-mu 1212. If you want to spend more than $200 I suggest a firewire or external DAC solution. Technically the e-mus are professional audio cards but they're perfect for the requirements you've stated above. Good drivers (including ASIO), lots of community support, even a community of modders for the tweak-crazy :)
The head-fi computers as source forums have a lot of information including featured reviews of these two cards which will explain why people like them. The high quality DACs and the ability to have non-resampled audio in particular make this a good choice if you want an internal PCI audio card.
Try Lynx Studio Technology, M-Audio or RME-Audio for hi-end soundcards.
For USB to Digital Coax/RCA interface converters;
Xitel Pro-HiFi-Link or Empirical Audio USB Off-Ramp & Freeway.
Here's another vote for the E-Mu 1212M (or 0404M, I guess). The difference in audio quality between one of these and your typical Audigy/Soundblaster card is HUGE.