Investing Beyond Contribution Limits

What is the best way for me to invest beyond the current contribution limits?

Since the market has been down the past couple of years, I see this as a good time to make investments. My problem now is that I am maxing out my 401K contributions and already have maxed out my yearly IRA investments.

What is the best way for me to continue investing in this down market? Is there a logical next step or is it just a matter of choosing the type of investment I think will do the best?

Are there more tax breaks for certain types of investments?

I guess my initial thought is to open an online investment account and begin to invest in individual companies. Actually, I would prefer to invest in an index fund to diversify my risk.

I have never maxed out my contributions before so investing beyond the 401K and IRA vehicles is something new to me.