Actually, according to the S&P 500, stock prices have never been higher, in nominal terms. In real terms (data from Prof. Shiller of Yale), the S&P 500 price level is at the 3rd highest point it's ever been. The first highest was at the height of the tech boom, and the second highest was at the height of the real estate boom. But the issue is not only the height of the price level, it's the relative height. In general, we prefer to look at normalized price measures, like price-to-earnings ratios (P/E). Earnings are defined as the trailing-twelve-months net income divided by shares outstanding. In real terms, P/E right now is 23.5 (again from Prof. Shiller's data), and the long-run average (going back to the late 19th century) is 16.5. The 60-month moving average of the P/E is 20.42. That means the P/E (and so price) is relatively high.
There are some reasonable arguments for a higher P/E. The first is that fundamentals (earnings, growth, dividends) are expected to be higher in the future. While this is possible, it is not normally the case empirically speaking. In the data, higher prices are followed by low returns, not by higher earnings/growth/dividends. Earnings are certainly doing well, as they recently reached one of their highest points (in real terms) since the late 19th century. But earnings aren't the whole story, growth is also important. There is good evidence that one source of higher earnings was reduced investment, which will compromise future growth. Now, investment has recovered, and earnings have turned downward, so we'll see what happens there.
Another factor that can drive up stock prices is a reduction in the required return. Required return is composed of the risk-free rate, plus risk factors. Required return can decrease because the risk-free rate goes down (we know this has happened, but is starting to increase again). It can also decrease because: risk decreases (not buying that story) or risk aversion decreases (meaning people require a lower risk premium for a given level of risk). Many people, me included, would argue the risk-free rate is abnormally low right now and that's driving at least some of the price increase. There is also evidence the equity risk premium is abnormally low right now, but that's usually estimated using price data, so it is rather mechanical and therefore I don't like to appeal to that argument.
In my view, stock prices are relatively high right now. What should we expect if that's the case? We should expect future long-term returns to be relatively low. That means, given dividends are stable, stock prices will drop. Now there are several moves one can make to take advantage a price drop. First, you can short specific stocks, or the whole market (SPDR S&P 500 tracking shares, for example). Second, you can buy put options on same (recognizing that puts expire!). Third, you can go long on commodities that tend to do well in market crashes, like gold & silver.
The problem with any short position is that you may lose money before you make money, since the timing of the market downturn is anything but certain. So when your options expire out-of-the-money, you'll lose the premium. A short position could get called, and you may have to buy back at a loss. At least long positions can be held for much longer than shorts, so those are less risky in that sense. Of course, if you think I'm wrong, the answer is simple: go long on stocks! But don't say I didn't warn you.