Since strategies are one of the fundamental game genres, among them you can find RTS and TBS, which can only be played online. Often they are available only in the browser, which has its own advantage: you don’t need to download any client, nor do you need to pay any money (after all, such games are most often free).
This list contains all the online strategies that you can try right now. It includes both browser strategies and client RTS and TBS.