Grad school with low undergrad GPA I'm hoping to apply to grad schools this fall.  I think I'm a reasonably good candidate, one aspect aside -- I have around a 2.5 undergraduate GPA in-major and failed several math classes in college.
That was a few years ago.  In the mean time, I worked in industry for a while, and after that, I took two years of graduate-level classes and enrolled in a third, earning a 4.0 GPA and passing all the qualifying exams here; as I understand it, the remaining requirements for the MA degree are basically formalities.  
If I need to, I can stay in my current program -- I am enrolled in the MA/Ph.D. track -- but the one professor closest to my interests is retiring and doesn't want to take on any more students, and the next-nearest areas are very far afield of what I want to do.  I know that it's possible to get a professor to supervise a dissertation in an area that's not his/her specialty, but there don't seem to be any who want to do this, and at any rate I wouldn't have any other students to talk shop with.
I have some original, though not spectacular, results, although I'm having trouble corralling my coauthors to get things written up.  I think I'm looking to take another year or so of courses before starting on my dissertation just to catch up with enough background to read papers in the field.
There's a lot of advice out there for people trying to get in to grad school, but most of it seems to start with "Make a 4.0 GPA in-major or don't bother."  Does anyone have specific advice for someone in my situation?  I don't want to spend a bunch of money on application fees just to have my applications discarded by a secretary before the admissions committee even looks at it.
Also, please share any advice pertaining to low undergrad GPAs, even if it isn't directly relevant to my particular situation -- there are other people out there with similar issues, and this will probably be the first thing that comes up when they hit Google looking for help.
UPDATE: I ended up getting into about half the schools I applied to, including several of my top choices!  I even got some fellowship offers.  If anyone out there is in a similar situation, feel free to contact me.
UPDATE: In response to some questions, here's some information about my application and results:
http://www.mathematicsgre.com/viewtopic.php?f=1&t=685&p=3643#p3643
Unfortunately I don't currently have access to the hard drive that all my application materials were stored on so I can't say a whole lot else.  And I've just checked and it should be possible to contact me through the email linked from my profile.
 A: Well, first I want to ask a question: are you officially enrolled as a master's student at your current institution or not?  When you say that the remaining requirements for the master's degree are "formalities", do you mean that you've already done all the challenging stuff and still need to take a language exam / one more required course / something like that, or do you mean that you are not on track to getting a master's degree because you are not actually enrolled as a graduate student?
If you are enrolled as a graduate student, then...how did that happen?  It seems like you already surmounted the problem of low undergraduate GPA if you are currently in a PhD program.  What leverage did you have to get into this one program?
Anyway, when I read the first paragraph of your message I was quite pessimistic: a 2.5 GPA with some failed math classes is, as you seem to realize, a very poor record that would stop you from being admitted to most of the top 50-100 PhD programs in the US.  But then your story gets much better: if you are indeed on track to complete a master's degree with a perfect GPA and your current institution is willing to accept you as a PhD student, then the faculty who write your recommendation letters will say that they know you can succeed in math graduate school because you have already done so.  That will put you ahead of many applicants, believe me.
In general, when you've already spent some time in a masters / PhD program in mathematics and are trying to transfer into a different such program, most graduate committees will weight your performance in your current program much more strongly than your undergraduate performance, especially if the latter is more than a few years in the past.  So based on what you've said I don't think you should have too much trouble transferring to a PhD program of roughly equal quality to the program you're already in but don't find compatible with your research interests.  If you already have a truly substantial / impressive result then that puts you ahead of almost all entering PhD students of any quality, and you should be thinking of applying to the very top programs.  Without that, I think that honestly you will have difficulty getting into a top 10 graduate program with your record, because for these schools the competition is so keen that they can pick among candidates whose applications are completely without flaw.  But very respectable programs should still be possible.  For instance, based on what you've said your application to UGA would be seriously considered, and I encourage you to apply here if you are interested in number theory / geometry / algebra.
