In this paper, we derive general formulas to express the product of two theta functions as linear combinations of other products of theta functions. Several known theta function identities follow immediately from our formulas. In fact, we derive many identities for certain products of special cases of theta functions defined by Ramanujan and also we establish several modular relations for Rogers-Ramanujan functions, septic, nonic and dodecic analogues of the Rogers-Ramanujan functions.