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We generalize Cuckoo Hashing [16] to d-ary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + 驴) n memory cells, for any constant 驴 0. Assuming uniform hashing, accessing or deleting table entries takes at most d = O(ln 1/驴) probes and the expected amortized insertion time is constant. This is the first dictionary that has worst case constant access time and expected constant update time, works with (1+驴) n space, and supports satellite information. Experiments indicate that d = 4 choices suffice for 驴 驴 0.03. We also describe a hash table data structure using explicit constant time hash functions, using at most d = O(ln2 1/驴) probes in the worst case.A corollary is an expected linear time algorithm for finding maximum cardinality matchings in a rather natural model of sparse random bipartite graphs.