A model called "colored percolation" has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability p and are then colored by one of the n distinct colors using uniform probability q=1/n. Denoting different colors by the letters of the Roman alphabet, we have studied different versions of the model like AB,ABC,ABCD,ABCDE,... etc. Here, only those lattice bonds having two different colored atoms at the ends are defined as connected. The percolation threshold p_{c}(n) asymptotically converges to its limiting value of p_{c} as 1/n. The model has been generalized by introducing a preference towards a subset of colors when m out of n colors are selected with probability q/m each and the rest of the colors are selected with probability (1-q)/(n-m). It has been observed that p_{c}(q,m) depends nontrivially on q and has a minimum at q_{min}=m/n. In another generalization the fractions of bonds between similarly and dissimilarly colored atoms have been treated as independent parameters. Phase diagrams in this parameter space have been drawn exhibiting percolating and nonpercolating phases.