The cause of the GFC was that because credit was so readily given to those whom had no chance of paying it back, on the hope that their house prices would go up so they could refinance their loans with the increased equity. These sub-prime mortgages themselves were bundled into bonds at I think BBB ratings. Then you have some smart bankers packaging many of these different sub-prime bonds into a CDO, and got them rated AAA when the underlying asset class of the security was... someone who couldn't pay their home loan unless it went up in value.
That itself wasn't what caused the GFC, what caused it was that institutions all over the world bought these CDOs. When the borrowers began defaulting on their mortgages, the underlying asset of those sub-prime bonds, which were the underlying assets of the CDOs went bust. It had a global effect because everyone bought them.
The 'stock market bubble' at present is entirely different so I don't think it's really analogous to the GFC. For one, not everyone owns US stocks to the same extent that they owned the CDO's (unless I'm mistaken?). Even if many people do, it's not like Apple or Google will go bust if the stock market bursts, so institutional investors won't lose the underlying asset, which will regain its value overtime. You can see how this is radically different from the housing crisis.
The problem with the stock market is that the artificially low interest rates the Fed is maintaining (true for every Central Bank) promote excessively cheap credit. This promotes a misallocation of resources, and those who get that free credit are often large banks, large corporations, wealthy people, etc, before your average consumer. When these institutions get cheap money they typically want to invest it in capital projects. These projects increase the value of the company, which in turn raises the share price (since executives don't tend to invest in projects which generate negative value). Capital projects require additional employees which promotes employment, and those people take their wages and spend it. The classic upwards trend and 'multiplier effect'. This sounds nice, except those capital projects are a misallocation of resources, and eventually when the bust occurs liquidation of a lot of these projects and assets occurs, unemployment ensues, etc - this is because during the boom the PPF gets pushed out for both capital and consumer goods, so prima facie these companies seem justified. When the bust occurs, the capital goods remain but consumer demand recedes, and you're left with capital goods which are supposed to produce consumers goods for those consumers who just lost their jobs and are unwilling to spend. Quantitative Easing doesn't work here since it is those big players which get the money first, and they don't buy consumer goods.
Due to the misallocation of resources it must bust eventually, and that is the only reason a 'bubble' exists - the assets are being overvalued as the income they are generating based on present demand will be reduced during the bust, and so those assets too will devalue and be liquidated, causing a reduction in stock prices over and above the lack of confidence in the market.
The Q is when, and that really depends. First however, I think it is of no benefit to say that the stock market is the highest its ever been and that that's a problem. Economic growth occurs, the stock market will always be higher because of that (the underlying assets which the stocks represent are greater). The Q is how much of a premium are we paying from the proper valuation of those stocks. Also that volatility is greater in today's market I think is also of little benefit as a diagnostic symptom. The world is getting more and more competitive (so companies don't last as long as they use to), and people have access to more and more information which means stock prices are more sensitive to current events. Considering the blockbuster that was this year, volatility is to be expected, and it doesn't really change the fundamental question as to what the premium for the stock market overall is, relative to its sensible valuation.
How big an effect interest rates have is a big question. Unfortunately an interest rate rise will probably occur in conjunction with a Trump Presidency - that'll be sure to send shivers down investors spines. Anyway, people know interest rates are artificially low, and so I would hope they have been priced in by executives and investors which would mitigate the harshness of a rate rise. It also depends on how sensitive mortgage payers are to interest rate rises. Obviously a tightening up of credit means less capital projects which means less spending, less employment, less spending more, etc, and you have that classic downtrend - in the mean time companies consolidate, and those companies that weathered the storm purchase those liquidated assets (this is why a correction is vital).
Unless there are other unknown factors, the impending bust won't be as large as the GFC. It will however have enormous social ramifications, especially given the widening income inequality. You wipe off half the value of wealthy peoples assets, nothing much happens to them. What happens to the average consumer though is that they have no job, and that will feed into the social justice rhetoric in our time. From a purely economic perspective though, the stock market bubble won't hit GFC levels - to repeat during the GFC, debt went bad. Debt is simply an obligation to repay, and when people no longer want to repay, the debt vanishes. Equity is different however, because its underlying value is backed by some assets which can be liquidated. Consequently, since the stock market boom is equity-based, it's not going to be particularly bad.
Not sure why I wrote an essay...
It is totally worthless and an increasing number of people are becoming aware of that fact. 
