This of course is not for myself, but for my girl friend, who has yet to shoot a gun. An apartment adjacent to hers was recently robbed by 3 assailants who over powered the owner of the apartment after they knocked on his door. A month ago, she actually called the police on three men who were snooping around her place, and apparently, her description fit the victim's description. These guys have a lot of balls, so I wouldn't be surprised if they tried again.

Regardless, she has never shot a gun yet. I think it would be stupid for her to run out and buy one, especially considering that she does not have a conceal carry permit. I think in Indiana, a conceal carry permit is required to carry a taser. I'm not sure about stun guns. Doing a quick web search, I'm not a fan of most of the websites I've come across nor the products they sell. They look to cheap and sleazy for my tastes.

Do you guys have any recommendations? I was thinking of something like a collapsible baton or a Surefire style light that doubles as a stun gun. I really wish Surefire made something. I'm definitely making it a point to teach her how to shoot and take her to a Gunsite class in Indiana this Spring (assuming she's ready by then). She will be applying for a conceal carry permit soon.

Yeesh, generally I would be really hesitant to recommend a "stun gun" to anyone for self defense, but the scenario you named ( 3 home invaders) definitely calls for no less than a firearm.
Get her permit, get her trained and ger her a good, reliable firearm that she is confident and proficient with. Training is paramount (not just standing still and shooting holes in paper, but movement, cover, reload drills and of course some combat accuracy stuff.
Thats my 2 cents.

This.  If the recent event of three home invaders is the reason to get a Taser or stun gun, it is exactly the scenario that these devices dont work in.  Electronic devices are generally designed to work on one target, not multiples.  If she is serious then she needs real training, with a firearm.  

If your just the boyfriend who wants to protect his girlfriend and have her "feel safe" and she really has no interest in personal protection and its all coming from you, then carry on.  I think Taser offers training classes......

Thats not entirely accurate, the TASER X3 was designed for multiple assailants. It rotates NMI pulses across the firing bays to engage multiple targets simultaneously.
Here a little video: http://www.youtube.com/watch?v=n0PWcjDpTvE

Now, I am not saying an X3 is better than a firearm and in the situation that you feel your gf is in I would prefer a firearm to any non-lethal weapon. But there are options out there if your looking for a non-lethal option.

Have you decided on what your plan is for your gf?