We study opinion dynamics on complex social networks where each individual holding a binary opinion on a certain subject may change her/his mind to match the opinion of the majority. Two rules of interactions between individuals, termed as classic majority and influence majority rules, respectively, are imposed on the social networks. The former rule allows each individual to adopt an opinion following a simple majority of her/his immediate neighbors, while the latter one lets each individual calculate the influence of each opinion and choose to follow the more influential one. In this calculation, the influences of different opinions are counted as the sum of the influences of their respective opinion holders in neighborhood area, where the influence of each individual is conveniently estimated as the number of social connections s/he has. Our study reveals that in densely-connected social networks, all individuals tend to converge to having a single global consensus. In sparsely-connected networks, however, the systems may exhibit rich properties where coexistence of different opinions, and more interestingly, multiple steady states of coexistence can be observed. Further studies reveal that low-degree and high-degree nodes may play different roles in formulating the final steady state, including multi-steady states, of the systems under different opinion evolution rules. Such observations would help understand the complex dynamics of opinion evolution and coexistence in social systems.