In theory vegans do not need to take omega 3 supplements because there are many vegan foods with omega 3 in them, such as chia seeds or ground flaxseeds. Dr Michael Gregor recommends two tablespoons of ground flaxseeds per day to get your omega 3 requirements. However, the form of omega 3 in most plant food is ALA (alpha linoleic acid). DHA and EPA (which are important for brain function) can be made by the body using ALA, but the concern by some is that the conversion of ALA to DHA and EPA is not efficient.
The main sources of DHA and EPA are algae or fish. Fish get DHA and EPA from eating algae. The main concern with eating fish is the risk of industrial pollutants such as mercury. To avoid any concern about mercury, I take DHA and EPA supplements purchased off iHerb. These supplements contain DHA and EPA from algae grown on land in controlled conditions ensuring no industrial contaminants.
I am personally using the Deva Omega 3 DHA-EPA I have purchased off iHerb, but if there is one criticism I have it is that they have a very fishy taste and the capsules seem moist when you touch it. I have tried other omega 3 supplements that don't seem to have this issue, such as the Source Naturals vegan omega 3 brand.