I wouldn't have a problem with living forever. For one thing, we tend to forget the past, so we never really feel like we've lived as long as we have. Have you ever noticed almost every old person will talk about how time flies by faster than we expect? That's because we live in the present. Can you remember many details about what you were doing 10 years ago? I sure can't.
About becoming bored. I remember a saying my dad had: "The only people who are bored are boring people." That's a sentiment I agree with. The pursuit of happiness and knowledge holds enough challenge to keep anyone from getting bored, no matter how much time is spent.
In the end though, we're all filtered through the same bottleneck of death, or rather change. None of us really cease to exist, we just change forms. Nothing is ever gained or lost, just changed.