Definition: An organometallic compound is one that contains at least one direct metal–carbon bond, where the carbon atom belongs to an organic moiety (e.g., alkyl, aryl, carbene, carbonyl, etc.). Metalloids such as B, Si, Ge, As, Sb are also considered under the purview of organometallic chemistry.
Example with no M–C bond: Wilkinson's Catalyst — [RhCl(PPh3)3]. In this compound, Rh is bonded to Cl and to P atoms of the triphenylphosphine ligands; there is no direct Rh–C bond. Despite this, it is classified as organometallic because the PPh3 ligands are organophosphorus in nature and the compound is central to organometallic chemistry. Another valid example is Ti(OCH2CH3)4 where Ti is bonded to O, not C.