The short answer is no, there is no need to get into any other funds. For all intents and purposes the S&P 500 is "The Stock Market". The news media may quote the Dow when the market reaches new highs or crashes but all of the Dow 30 stocks are included in the S&P 500.
The S&P is also marketcap weighted, which means that it owns in higher proportion the big "Blue Chip" stocks more than the smaller less known companies. To explain, the top 10 holdings in the S&P represent 18% of the total index, while the bottom 10 only represent 0.17% (less than 1 percent). They do have an equal weighted S&P in which all 500 companies represent only 1/500th of the index and that is technically even more diversified but in actuality it makes it more volatile because it has a higher concentration of those smaller less known companies. So it will tend to perform better during up markets and worse during down markets.
As far as diversification into different asset classes or other countries, that's non-sense. The S&P 500 has companies in it that give you that exposure. For example, it includes companies that directly benefit from rising oil prices, rising gold prices, etc known as the Energy and Materials sector. It also includes companies that own malls, apartment complexes, etc. known as the Real Estate sector. And as far as other countries, most of the companies in the S&P are multi-national companies, meaning that they do business over seas in many parts of the world. Apple and FaceBook for example sell their products in many different countries. So you don't need to invest any of your money into an Emerging Market fund or an Asia Fund because most of our companies are already doing business in those parts of the world. Likewise, you don't need to specifically invest into a real estate or gold fund.
As far as bonds go, if you're in your twenties you have no need for them either. Why, because the S&P 500 also pays you dividends and these dividends grow over time. So for example, if Microsoft increases its dividend payment by 100% over a ten year period , all of the shares you buy today at a 2.5% yield will, in 10 years, have a higher 5% yield. A bond on the other hand will never increase its yield over time. If it pays out 4%, that's all it will ever pay.
You want to invest because you want to grow your money and if you want to invest passively the fastest way to do that is through index ETFs like the $SPY, $IVV, and $RSP. Also look into the $XIV, it's an inverse VIX ETF, it moves 5x faster than the S&P in the same direction. If you want to actively trade your money, you can grow it even faster by getting into things like options, highly volatile penny stocks, shorting stocks, and futures. Don't get involved in FX or currency trading, unless it through futures.