I simply think people should have the right to end their own lives if they choose.
That's not to say people shouldn't take steps to protect loved ones against their own depressions and self destructiveness, but in the few countries that do have assisted suicide programs, there are safeguards in place for those very reasons.
For example, in Denmark, two qualified doctors need to evaluate the sick/elderly and both come to the same conclusion that they are not motivated by any kind of mental issues or depression that is clouding their judgement, and those two doctors aren't allowed to confer with eachother.
The anti-euthanasia crowd will often suggest various ways in which assisted suicide programs could be used to push death on the unwanted eldery, take advantage of the weak and sick, etc. But when you look at the programs in other countries, it all seems to be set up very well to safeguard against exactly that.
As for anyone who argues the religious angle, saying that a person doesn't know what if anything awaits them after death, and how they will be judged for something like suicide, I say surely that's their own choice and nobody elses.
You can't use your own beliefs to dictate how people end their lives any more than you can dictate how they live their lives.