While I absolutely hate that we have to resort to euthanasia, I say yes, it should be legal, considering the way our society is right now.
There are too many people who buy puppies thinking they'll love that puppy forever but then can't take care of it after it grows up and then leaves the pet in the pound/animal center/what-have-you. What this means is that those very pounds simply don't have enough room to house all the animals coming in, while still being able to care for all the animals they already have -- because there aren't enough people adopting -- so the only way to make room for new pets, and ones that have a better chance of getting adopted, is to euthanize the ones that have little to no chance of getting adopted.
It is the saddest reality, but for now it is a measure people take simply because there is no other reasonable choice.
---------- Post added at 07:33 AM ---------- Previous post was at 07:29 AM ----------
Oh wow, I thought this was in regards to animals.
Well, with humans... hm. There are things similar to euthanasia for humans already -- like the death sentence, and removing someone from life support. In my mind, euthanasia on a conscious human being who did not commit a heinous crime would be OK if the person in question is at least reasonably sane and genuinely wishes it for themselves, and has had ample time to consider the gravity of the situation (so no euthanasia for people suffering a momentary breakdown and ask for it in the heat of the moment).