Along with cabbage, Brussels sprouts, and other green leafy vegetables, spinach has a lot of vitamin K, which can affect how warfarin (Coumadin, Jantoven) works. It's OK to eat those veggies when you're taking it, but try to eat the same amount every day. A sudden boost of vitamin K can make warfarin less effective.
Newer blood thinners -- apixaban (Eliquis), dabigatran (Pradaxa), edoxaban (Savaysa), or rivaroxaban (Xarelto) -- work differently. They block various points in the series of events that form a clot. And you can eat green leafy vegetables whenever you want.