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We use rook placements to prove Spivey's Bell number formula and otheridentities related to it, in particular, some convolution identities involvingStirling numbers and relations involving Bell numbers. To cover as many specialcases as possible, we work on the generalized Stirling numbers that arise fromthe rook model of Goldman and Haglund. An alternative combinatorialinterpretation for the Type II generalized $q$-Stirling numbers of Remmel andWachs is also introduced in which the method used to obtain the earlieridentities can be adapted easily.

Rook theoretic proofs of some identities related to Spivey's Bell number formula