Not sure about demo accounts per se, but if you open an account at most firms today they have a demo trading account available. For stocks and options I use Optionshouse, for futures I like Infinity. Both are fairly simple and cut down to the basics systems, but that is how I like it. I don't trade stocks anymore, but when I did I liked Firstrade; their platform is (or was) pretty basic.
Check out the websites of various brokers, some even give you a trial period where you can open an account without funding for a short period.
The most helpful demo will be dependant on your trading style and what you are looking for. Trademonster has a decent demo, but I prefer the others listed.
Good luck.