Best paper trading I have ever found on the web (simple, effective, interesting, very well made, no need to install anything):
www.chartgame.com
Emotionally, it is not realistic, because you can speed up time, but it's still paper trading, and the regular paper trading (in real time) for most people is too boring and slow. So, rather than quit at that, you might as well keep at the less realistic one, which still teaches you a lot.
Second best: Genesis Trade Navigator: it has a paper trading feature, very good one because you can trade futures with it in playback mode, so you can speed it up as well, which you can't do anywhere else I know of, with futures i mean. It has a free trial of about one month, and the software is heavy and kind of user unfriendly.
Yet, despite trying both of those simulators, and IB paper trading account (in real time, totally realistic, in this sense the best of all), I could never become profitable. But at least those simulators save you a lot of money, if you use them. I didn't use them for the first 12 years, but then they did save me money.
Overall, I think it's rare to be one of those guys who can be profitable at discretionary trading. If you don't have what it takes, it's almost impossible to become profitable at discretionary trading. On the other hand, system trading is much easier. So I'd advise everyone to start directly with that.