PC

A PC is an excellent platform for multimedia.
In case of audio, you don't need much power for playback.

There are many different strategies to obtain best sound quality.

You can choose between a sound card or an outboard DAC

 

If the PC is located close to your audio silent operation is required.

Laptop or desktop

In general laptop's make less noise but there are exceptions to this rule.
You lack the space to add a soundcard of your choice to a laptop.
You need an outboard DAC if you want to improve on sound quality.

Storage

HD’s can make a considerable noise.
In general the 2.5" are quitter.
SSD (Solid State Disk) is the ideal choice, no moving parts at all.
Probably 4 times as expensive as HD’s but HD’s has become pretty cheap.

HTPC

Kubb Fanless

There are Home Theatre PC's build with silence in mind.

In general passive cooling.

Performance

For playback you don't need much power. Any MP3 player or cellular phone proves this point.
Browsing your library might require some power depending on the efficiency of the media player.
Real time converting PCM to DSD is taxing but you might wonder if you have any good reason to do so.

 

Intel NUC

Intel NUC Kit NUC5PGYH - Pentium N3700 / 2 GB RAM / 32 GB SSD / Windows 10 € 297,99

Intel® NUC Mini PC NUC5PGYH is the first offered as a complete system by Intel. A complete Mini PC in a tiny but mighty package, this Intel® NUC with a quad-core Intel® Pentium processor delivers the same performance and visuals you can get in a full sized tower. The system is preinstalled with Windows® 10, giving you the latest Windows right out of the box. 8-channel audio, built-in WiFi, and Bluetooth along with HDMI and wireless display capabilities makes NUC5PGYH an excellent HTPC. The NUC5PGYH also includes 32 GB of on-board storage, with room for an SSD or HDD drive for storing all your music, media, and other data.

Source: Intel

Added 2015

Music server

A music server is a PC dressed up as audio gear.
More about music servers can be found here.

Parts

You can get all kind of parts to reduce noise level.

Big, low speed fans make less noise.

Passive cooling makes no noise at all.

 

Streacom DB4 fanless ITX case

 

Motherboard

Gigabyte is the first company known to me selling a mobo with audio quality as a sales argument.
It features a dedicated USB port with clean power.
The onboard audio has socketed op-amps and adjustable gain.
They also claim to shield the analog components from noise at PCB level.

Gigabytes GA-H81.Amp-UP

Raspberry Pi

A very popular platform.

Almost the "default" recommendation on many audio forums.

More...

References