Can I put a 10 speed 11-36 cassette on a Road Bike with a 50/39/30 crank? I have a road bike with a Shimano 10 speed 105 group (2007).  It has a triple 50-39-30 crank. I want to put a 11-36 cassette maybe the Shimano Deore XT CS-M771 10-Speed Cassette  (Note: I can’t find an 12-36 cassette for sale).  The way I understand capacity  I would need 45t (50+36=86 30+11=41 86-41=45).

First is the shift ratio of my 2007 Shimano 105 10 speed shifters compatible with the derailleurs listed below:

The Shimano Deore XT RD-M772-SGS Shadow Rear Derailleur appears to have the 45t capacity but is rated for 34t max cog.  

The Shimano XT RD-M780 Shadow Rear Derailleur SGS is rated for a 36t max cog but only has a 43t capacity.

Harris Cyclery list their Shimano XT RD-M772 Shadow SGS Rear Derailleur Top Normal as having a 36t max cog, this may be an error or what they have successfully run.  They want full list price of $129.95.
Most likely yes, the M772 will work.  As you have already calculated, the capacity is within spec, and the maximum sprocket size is out of range by just 2 teeth.  In my experience this is very likely to work, so long as the rear dropout on your frame is not especially near to the axle, and so long as you tighten the "B screw" more than normal with a smaller cassette.

Whatever you do, don't buy a "Dyna-Sys" model, because they aren't compatible with your shifters.  This rules out the M780.

Also note that with the super-low gear of 30x36, you do somewhat increase the chances of breaking a rear spoke (or the chain) if you put a large amount of force into the pedals with such low gearing.  This isn't a big concern, but don't get carried away with it unless your body weight is quite low.