The maximum $k$-colorable subgraph problem ($k$-MCSP) is to color as many vertices as possible with at most $k$ colors, such that no two adjacent vertices share the same color. We consider online algorithms for this $\mathcal{NP}$-hard problem, and give bounds on their competitive ratio. We then consider a large family $\cal{A}$ of online sequential coloring algorithms and determine the smallest graphs for which no algorithm in $\cal{A}$ can produce an optimal solution to the $k$-MCSP. We then compare the performance of several online sequential coloring algorithms, using DIMACS benchmark instances. We finally consider the case where vertices colored at an early stage can receive a new color later on, as long as they remain colored.