The National Osteoporosis Foundation states that one in every two females age 50 and older will suffer an osteoporosis related fracture.
A little known fact, is that doing flexion based exercises, such as crunches or sit-ups will increase your risk of having a spinal compression fracture than if you do NOT exercise at all (Sinaki, 1984 - a doctor that does research at the Mayo Clinic). This fact is true of people with osteoporosis but not true for people without osteoporosis.
If you have osteoporosis to strengthen your core safely, planks and doing modified pilates (without lifting your head) are good options. However if you are looking for a quick, fun core workout which you can do at home without flexing your spine please check out the free video OSTEO Ab Blast on YouTube, just search for PILATES MiniMAX.