According to the IMF, a "global recession" would mean that real GDP growth for the whole world was less than 3%, and by this definition there have been six since 1970: 1974-1975, 1980-1983, 1990-1993, 1998, 2001-2002, and 2008-2009.
You'll notice that the U.S. had recessions during all of those periods, except 1998 when we were on fire. So the world can easily have a global recession, with or without us.
The most likely even to trigger another global recession would be if Europe falls off a cliff, which is not a very outlandish scenario. However, Europe will probably keep grinding through the rest of this decade and weighing everything down, while the U.S. keeps chugging along, with developing countries rollercoastering.
I do expect a minor recession in the U.S. sometime before the end of this decade, but I don't expect it to be anywhere near as bad as the Great Recession, let alone cause a global recession.
I'm amused at all the posts that say there won't be another global recession for a decade or more. If you look at the list in the post I've quoted, then it's pretty clear that the longest period in the last 40+ years without a global recession was seven years from 1983 to 1990. We are almost 6 years past the end of the last recession. Adding another decade would make it a record recovery period by more than double the historical best. That seems farfetched to me.
Statistically the most likely answer is that the next global recession is due within a year. Since 2008-09 was the most severe recession on the list, it is more likely that the next one will not be as severe.