Spinach, like cabbage, Brussels sprouts, and other green leafy vegetables, has a lot of vitamin K, which can affect how Coumadin works.
If you take that drug, it's OK to eat those vegetables, but try to eat the same amount every day. A sudden increase in vitamin K can make Coumadin less effective.
If you're taking any of the newer blood thinners -- Eliquis (apixaban), Pradaxa (dabigatran), or Xarelto (rivaroxaban) -- you can eat as many green leafy vegetables as you'd like. Your diet won't affect those drugs.