It is shown that a careful study of the simplest family of generalized Clifford algebras (GCAs) associated with the $N$-th root of unity in $d$-dimensions leads to the following generalized anti-commutator with $ N$ entries $ { e_{i_1}, e_{i_2}, e_{ i_3}, ldots, e_{ i_N} } = e_{i_1} e_{i_2} e_{ i_3} ldots e_{ i_N} + permutations = N! eta_{ i_1 i_2 ldots i_N } e $, where $e$ is the unit element and all the $ N !$ terms of the permutations appear with the same positive sign. The components of the rank-$N$ metric are $ eta_{ i_1 i_2 ldots i_N } = 1, $ iff $ i_1 = i_2 = i_3 ldots = i_ N $, and $0$ otherwise. The range of the indices $ i_1, i_2, ldots i_N $ is $ 1,2, ldots, d $. We proceed to explore the $N$-th norm extensions of the quadratic norm and write down a generalized Finsler-like arc-length based on the rank-$N$ metric $ g_{mu_1 mu_2 ldots mu_N}$. We continue by constructing the different expressions of the Dirac operators associated with the (Generalized) Clifford Spaces corresponding to these GCA's. Dirac operators are essential in the study of Spectral Geometry in Noncommutative Geometry after imposing the correspondence between the geodesic distance and the inverse of the Dirac operator (a fermion propagator). These generalized anti-commutators above are special types of an $N$-ary algebraic structure. We finalize by displaying the relation among GCAs and the algebras underlying the noncommutative fuzzy torus and discuss applications in condensed matter and quantum groups. We conclude with some remarks on $N$-ary algebras and their applications in Mathematics and Physics.