from the medical side, if your on coumadin (warfarin) you probably have some cardiac issues going on, which isn't cheap, and would be a big red flag....
I'm no expert here but If nothing else I'd imaging that the need for that sort of medication would be an indicator of a major pre-existing heart condition, and yes that will make them run the other way.
It depends on why you're taking the medication. Most major medical insurance companies have similar underwriting criteria, but some will rider a condition and still issue a policy, or will determine a rate-up based on your health history,height,weight,age,etc.
There are companies out there that will issue anyone a policy no matter what their health history. I'd contact a local independent agent in your state for the specifics.