A big part of learning to fly on instruments is procedures: quickly reading a chart and making the appropriate turns, radio changes, power changes, etc in the 5–10 minutes you're flying an approach. It's important to train in a real plane but an instrument student can learn a lot with a simulator, even a basic PC game.
Simulator: For 20+ years Microsoft Flight Simulator was the gold standard, but Microsoft has abandoned the product and recent iterations like FSX didn't work very well. X-Plane is the new hotness and works on PCs, Macs, and even iOS devices. It's pretty and has neat aerodynamic simulations but what really makes it work for IR training is that it simulates the panel instruments pretty well. CDI needles move smoothly, VORs warble just like the real thing, and it has a good simulation of clouds and the moment of breaking out of them. You can easily customize your plane's panel, too. X-Plane is pleasant software where FSX always felt awkward.
GPS: X-Plane has some fancy avionics simulations but the GPS options are terrible. The solution is Reality XP's Garmin 430W/530W. It's a bridge to Garmin's standalone 400W/500W trainer, simulating the most popular high end GA GPS. The realism is fantastic; it feels like it's emulating the hardware and running the actual firmware. The only drawback is the navigation database is from 2007. Not a big deal, but newer approaches may be missing and sometimes it's out of sync with X-Plane's database.
ATC: Learning to fly IFR requires learning to work with air traffic control; you can't really simulate that. So enthusiasts have been operating VATSIM, an ATC network staffed with volunteer controllers. VATSIM's quality apparently varies, there's a new modestly commercial effort called PilotEdge that looks promising.
Other addons: X-Plane has a robust third party developer community creating model aircraft, better scenery, and various plugin code. Unfortunately X-Plane.org is very poorly organized, hard to find things. I haven't seen anything there I've had to have although I am excited for RealScenery NorCal. There's also rumours of software that imports Google Maps aerial photography to replace the default scenery but apparently it's banned. One neat thing is you can use XPlane's network mode to drive a live display of SkyCharts on your iPhone or iPad.
Hardware: X-Plane has a mouse mode but you really need a controller of some sort. I'm reasonably pleased with the Saitek yoke. I also have an older CH Products yoke which is nicely smaller but doesn't feel right. Honestly, neither feel right, I have a very hard time controlling the plane in the pitch axis. I'm beginning to think a fancy joystick would work better, if it doesn't feel like a real plane anyway why not go for something totally different?
Getting fancy: There's a whole world of very fancy amateur simulation products. People spend hundreds to thousands on avionics simulations, plane models, scenery, and flight controls. And if you're serious you've got 3–6 PCs networked together running X-Plane so you can look out the side window, too. That's all overkill for learning instrument procedures and for that kind of money I'd start looking into FAA Certified equipment. It may make sense if you want to "fly" a heavy jet, but for my purposes I'm happy with the PC game and then jumping in a real plane.