Anythings possible I guess. But that apparent alien on Mars that turned out to be a fancy rock/shadow sure didn't look very friendly.
When oil dries up and electricity can't be produced, and when the internet becomes a living creature and when a snowball has a chance in hell, then Google will go bankrupt.
It´s impossible to predict the future but in a short/medium term i think it´s radder impossible that google bankrupts (at least in normal conditions). Most probably it would split like said before. In a long term...well they have huge amounts of money but also lots of employees and stock holders eager to make more money with a % of power in the companies decisions... so IT`S possible but not likely if the internet market maintains it´s course. But´s all speculation, it´s impossible to predict.
Maybe the one guy that has all the google stock will basically take over the world or something. But overall google is so dominant in the market that the chances of bankruption are sooo low. Alot of people use their services.
I don't think Google will ever go bankrupt. Maybe one day go out of business or their services just stop being peoples first choice, but never completely broke...
Over a long enough period of time, no company will exist in its present form. Google will likely become something completely different than it is today, and people will say "remember when XYZ Corporation was called Google and only dealt with searching something called the internet? How antiquated!"
I don't think it will ever hapen in the immediate future, in 20 years who knows but right now they are earning millions a day so the chances of them going bust is highly unlikely.