How many backups of my seed phrase should I keep?

At least two, kept in separate secure locations, and ideally no more than three. Two copies in different places protect you against a single fire, flood, or misplacement, while keeping the number low limits the chance of theft. Each copy should be physical and offline, written clearly in order on paper or stamped into metal, never stored digitally. Avoid scattering many copies around, since every additional copy is another thing that could be found. A balanced approach defends against both losing the phrase and having it stolen, which are the two opposite dangers every backup plan must address at once.