When looking for the best free stock market game online, you should be looking for three things: whether or not you're dealing with realistic stock market data, if you can trade similarly to how you would trade in real life, and if there are incentives to keep you playing the game and keep it competitive with other players.
Many free stock market games are inadequate because they oftentimes don't give you realistic data to work with. At best, their data is delayed, but I've also see situations where data is just plain inaccurate and doesn't update frequently. Nothing gets more unrealistic than being able to make trades on data that is stale when you already know where the stock should be. Players often find these loopholes and exploit them for their own gain. Avoid stock market games like this at all cost!
Secondly, you want to make sure that you can actually trade like a normal trader would. By this I mean that you should be able to place intraday trades and be able to short the market when necessary. This might sound elementary, but the most popular free stock market game of the past few years - CNBC's Fantasy Stock Challenge - allowed neither. With the market swinging as wildly as it has been, not being able to use these professional market methods will hinder you from seriously learning and practicing necessary market trading techniques.
Lastly, (but possibly most importantly!), make sure there is an incentive to play the game! This might sound trite, but its easy to make little of your wins and losses in a free online stock trading game unless there are some prizes or rewards to shoot for. Many times, the competition between players for the prizes is what provides the extra edge for players to stick with an investing strategy and learn how to trade better!
