First, I've been attracted by the ability to run old and/or closed-source programs in their native environments. For instance, I've bought ages ago a nice electronic English dictionary for Windows. After my switch to linux, I was able to use it for a time via Wine, but at some place they broke the support of such 16-bits programs. And I will certainly not reboot my computer each time I want to search for a translation. So I now run a virtual Win98 machine using Qemu. This virtual machine also helps to check the rendering of this very web page by Internet Explorer. This point is not Windows-specific: old closed-source linux programs can benefit from emulation useful. Think for instance of a scientific software that rely on libc5: how many linux systems can still run it these days ? Even for open-source programs, emulation can be relevant: think of the difficulties to port openoffice from 32-bits to 64-bits (ok, in this particular example, a chroot environment is probably better suited than a complete emulation).
Then, for teaching compilers (or other hardware-related topics), it's really nice to consider first a clean assembly language, and in particular a RISC one, such as MIPS (see here for instance). But Mips machines aren't so common nowadays, so let's emulate! Moreover, this way, there is less risk of crashing the whole computer ;-).
Moreover, compilers are still an hot research topic. I'm currently involved in a project whose goal is to produce certified compilers. Once again, a RISC architecture (PowerPC) was chosen as target, both for simplicity and industrial relevance. Once again, without any PowerPC machine in the nearby, I've tried to emulate one.
Emulation can also bring additional security, thanks to isolation of different layers. For instance, my win98 machine can be attacked by a virus or worm, I (relatively) don't care: I've no sensible data in the virtual machine, the underlying linux host will hopefully not be affected, and anyway this attack cannot survive a reboot of the virtual machine since its image file is read-only (thanks to the snapshot feature of qemu). Of course, this security aspect isn't absolute: few emulators have been written with security as primary goal and few audits have been done on them. The Chroot example shows that sometimes one can evade from jail...
But of course, the main reason is ... it's fun !

Concerning the virtual machines presented below, the main goal is pedagogical: having access to a complete gcc compiler toolchain on something that isn't x86. So don't be surprise to end on a raw console. It was just enough for my needs. Up to you to install and run fancy graphical programs, and let me now if you succeed. Of course, the Win98 virtual machine is another story, but I cannot redistribute it, so I will just say a few work of it.

By the way, I would like to thank here all the developpers of these great emulators such as qemu, pearpc, gxemul, etc. Moreover, even if qemu's reputation is sometimes disputed amongst free software community, due to the existence of the proprietary kernel module kqemu, I would like to stress the fact that qemu itself is indeed free sotfware (more precisely LGPL). And kqemu is not necessary for the examples described here: it is designed to improve emulation of PC on PC, and even in this situation (e.g. Win98 on Linux) the emulation on a modern machine is quick enough without kqemu.