There's a huge difference between "can an anverage person make a profit on the stock market" and "can an average person get rich off the stock market".
It is certainly possible for an average person to profit, but of course you are unlikely to profit as much as the big Wall Street guys. An S&P 500 index fund, for instance, would be a pretty good way to profit. People with high-powered tools may make a lot of money picking individual stocks, and may even make some choices that help them when the market is down, but it's difficult to see how they could consistently make money over the long term without the S&P 500 also going up. The same applies, to varying extents, to various other index funds, ETFs, and mutual funds.
I agree with littleadv that there is no single "right" thing for everyone to do. My personal take is that index funds are a good bet, and I've seen a lot of people take that view on personal finance blogs, etc. (for whatever that's worth). One advantage of index funds that track major indexes (like the S&P 500) is that because they are and are perceived as macro-indicators of the overall economic situation, at least you're in the same boat as many other people. On one level, that means that if you lose money a lot of other investors are also losing money, and when large numbers of people start losing money, that makes governments take action, etc., to turn things around. On another level, the S&P 500 is a lot of big companies; if it goes down, some of those big companies are losing value, and they will use their big-company resources to gain value, and if they succeed, the index goes up again and you benefit.
In other words, index funds (and large mutual funds, ETFs, etc.) make investing less about what day-trading wonks focus on, which is trying to make a "hot choice" for a large gain. They make it more about hitching your wagon to an extremely large star that is powered by all the resources of extremely large companies, so that when those companies increase their value, you gain. The bigger the pool of people whose fortunes rise and fall with your own, the more you become part of an investment portfolio that is (I can't resist saying it) "too big to fail". That isn't to say that the S&P 500 can't lose value from time to time, but rather that if it does go down big and hard and stay there, you probably have bigger problems than losing money in the stock market (e.g., the US economy is collapsing and you should begin stockpiling bullets and canned food).