I think it depends on what it is. Some off-brand goods are very good and cheap while others are very bad. For example, I have been getting off-brand tissues recently and some of them are good, while others are quite bad. If I know an off-brand product is good, then I will buy it.
I don't go out of my way to buy off brand food items but do buy them. There usually isn't a substantial price savings either. Certain things I'll stay away from as the same quality and taste compared to the branded product isn't there.
It depends what it is. There are some things which doesn't matter what the brand is. I'll buy off-brand chips, because it's a lot cheaper and tastes pretty much the same, but I won't buy off-brand coke, because that tastes awful.