Oddly, one thing that's poorly implemented is remote access from another computer. For Mac OS X users, there's Tune Connect - a well designed control tool that fits with the iTunes design. For PC users the choice is somewhat less impressive, but the excellent Tunesremote-SE offers a full iTunes interface.
Android has a range of iTunes remote apps, many of which come with free and paid-for options. Our preference is Retune. It's free (though a donation is recommended), and offers a more fully-featured interface than many alternatives. All these remote options offer support for the Apple remote speaker protocol AirPlay, which is one of the key reasons we're using iTunes.
AirPlay is a networked speaker standard, so anything that supports it will appear in iTunes as a potential speaker output. AirPlay stays hidden until an AirPlay device appears on the network. Add one and an icon appears next to the volume control in iTunes. Click this and a list of all available AirPlay devices appears. You have individual control over which devices output sound and at what volume, or you can have sound output from all of them.
Apple would like you to buy dedicated AirPlay speakers, which you can do, but one alternative that we like is to install AirBubble for Android and use the device as a AirPlay extender connected to a hi-fi or speakers. If you have older Android devices at home, this is a good use for the lazy green things.
For PCs, you can use the horribly named Shairport4w. This is an open source project that turns any PC into an AirPlay target. It's just a 1.3MB executable, so can happily be left running on any system that could be used as a speaker output.
In Apple's usual idiotic way, iOS devices can't be made AirPlay targets, and it removes any apps that enable this, but if you own a jailbroken device we understand AirFloat will do the job.
Finally we'll mention AirFoil which costs $25. Installed on a Mac or Windows system, it enables you to direct the audio from any programs to almost any device, including AirPlay compatible speakers, Apple iOS devices and Android devices running its free app, so you can enjoy the delights of iPlayer or Spotify anywhere in your home.