Usually, organometallic compounds are considered to contain the M-C-H group.  The metal (M) in these species can either be a main group element or a transition metal.  Operationally, the definition of an organometallic compound is more relaxed to include also highly lipophilic complexes such as metal carbonyls and even metal alkoxides.
Organometallic compounds are mainly considered a special category because organic ligands are often sensitive to hydrolysis or oxidation, necessitating that organometallic chemistry employs more specialized preparative methods than was traditional in Werner-type complexes.  Synthetic methodology, especially the ability to manipulate complexes in solvents of low coordinating power, enabled the exploration of very weakly coordinating ligands such as hydrocarbons, H, and N.  Because the ligands are petrochemicals in some sense, the area of organometallic chemistry has greatly benefited from its relevance to industry.
* Examples: Cyclopentadienyliron dicarbonyl dimer (CH)Fe(CO)CH, ferrocene Fe(CH), molybdenum hexacarbonyl Mo(CO), triethylborane EtB, Tris(dibenzylideneacetone)dipalladium(0) Pd(dba))