The biggest worry for most professors I talk to in grant-funded fields (which is most of the natural sciences and engineering) is not getting grant funding and having to lay off some or all members of our research group. In Canada, biomedical grant application success rates are around 14% so this is a pretty big worry.
People who are pre-tenure or in organizational units where there is no tenure (which includes a lot of medical researchers) also have to worry about losing their job.
In the U.S., very few professors can get paid their whole 12-month salary without getting some grant funding to pay for it. Some universities will commit 75% of the professor's salary as "hard money"—these are the ones with the bigger teaching loads. Others will provide only 5% of the salary and expect the professor to get the rest through grant funding. If you can't do it, expect to get a pay cut or lose your job. This is the prevailing model at elite medical research institutions like Harvard Medical School, Johns Hopkins School of Medicine, or University of California, San Francisco.