"Up to about 20 grams of fish oil can be well tolerated by most adults. However, such high amounts may not be beneficial and the FDA recommends that consumers not exceed more than a total of 3 grams per day of EPA and DHA omega-3 fatty acids, with no more than 2 grams per day from a dietary supplement.
At very high doses fish oil may have adverse affects on the human immune system, though studies have not shown such an effect at the more typical doses people take, i.e. <=2mg/day of EPA+DHA. However, it may impact the immune of some animals who don't normally eat diets high in Omega-3s such as cats and dogs
I was watching a doco on life in Elizabethan England last week and the diet listed was much higher in fish than now, mostly because people couldn't eat animal meat on 3-4 days of the week because of religious restrictions. They ate fish at least 5-6 times a week. Flax seed (aka linseed), which is also high in omega-3s, was also a significant part of their diet.