Alot of people ask the question, "why bother writing emulators? why emulate a system when you can own the original?" etc... The motivation behind it is obviously going to be different for everyone, but I'll try to convey my reasons for (attempting) to write emulators, successfully or usuccessfully. Be aware that these are my personal opinions and motivation, there are obvious real advantages to emulators, such as using them to test games that are being written for a system that requires some sort of media, such as CD/DVD's or cartridges to be written to. There are many other reasons though, such as virtualization of operating systems, you know, Virtual PC, VMware etc...
First of all, let me just state that in my opinion, writing emulators is not the most rewarding hobby if you want to see immediate results and get immediate satisfaction, it takes alot of work to get any tangable output from an emulator. For me, this in itself is good motivation, as when you do get something working in an emulator, it feels much more rewarding, like you've really achieved something.
The other reasons why I try to write emulators are simple, I enjoy programming, I enjoy games, and I enjoy learning exactly what makes computers "tick", put all those together, and emulation seems the perfect hobby for me, which it is. Sometimes it is maddening, sometimes it makes your brain hurt, but these are all things which are necessary sacrifices.
The final reason is that I find the emulation scene very attractive, and one day, i hope to write (or atleast contribute to) an emulator that will actually be useful to someone, and not just a learning project for me. I look up to the authors of all emulators, but especially ones like the PCSX2, and Dolphin. One day, maybe I'll be knowledgable enough to do something to help out... *bwwwww*
At the end of the day, i do it because i personally find it fun, i would imagine that all emulator authors feel the same way, or else we wouldn't seen such an amazing amount of them out there today. I remember seeing a thread on the PCSX2 site, stating reasons why the authors chose to write the PCSX2, they said that they wanted to prove that PS2 emulation was possible, and they succeeded in that i think we all agree, but i digress.