Ground opening and swallowing people must be pretty rare. I can't find a single documented instance. Plenty of instances of people and even cars falling into cracks that open have been documented, but the cracks that open during earthquakes usually stay open until you shove dirt into them.
There are also plenty of cases of earth spewing itself out, though. Soil liquefaction causes water and sand to gush out, and when the water recedes there will be big piles of sand everywhere. While mixed with water, the soil can act just like quicksand, and can swallow cars and even parts of buildings.
Here's a video from New Zealand showing liquefaction taking place. It looks like plain water flowing, but it's actually full of sand.
Water can actually be a huge threat during and after an earthquake, as can the lack of it; dams and levees can collapse, large storage tanks can fail, rivers can change course due to shifts in ground level, and of course near large bodies of water you can get tsunamis. Then there's the threat of water contamination due to cracked water mains near broken sewer pipes or failed chemical storage facilities.
Finally, a damaged water distribution system can allow post-quake fires to get out of control. That's why San Franciscans always talk about the fire destroying the city in 1906, not the earthquake. Fire probably was probably responsible for at least 90% of the property destruction.
