Suppose a population of 250 crickets doubles in size every 3 months. How many crickets will there be after 2 years?

There are 12 months in a year, so 2 years is 2 * 12 = <<2*12=24>>24 months.

In three months, the population doubles, so after 24 months, the population will double 24 / 3 = <<24/3=8>>8 times.
Starting with a population of 250 crickets, after doubling 8 times, there will be 250 * 2^8 = 250 * 256 = <<250*256=64000>>64000 crickets. Answer: \boxed{64000}.