I spent an entire month in hospital. Had an entire month more or less 24/7 of free time then, apart from a few daily things. Almost went nuts from boredom, tried to get things done but the boredom killed all of my enthusiasm for it all, there were no deadlines to get me off my ass, to get me to get moving. Now if you lived for ten thousand years or so, the open world would likely be like that hospital- in that time you would have mastered every musical instrument, have every conceivable phd, diploma, doctorate and certificate, be fluent in every language.... whats left to do once you've done everything?
Also, many would probably stop bothering after the 6th instrument, the 20th diploma, etc- once you've done x varieties of the same thing, the remaining would likely be boring before you even start.
I don't think anyone has the psychological capability to last even a thousand years, the boredom, the realization that everyone you could love will either die, or living forever as you do, become bored and sick and tired of you, will likely lead to alot of loneliness and pain....
then theres the fact that you would lose the best thing of all in life- the capacity to find new experiences. It would just be variations of the same things you have already done countless times over and over again.
In short, I think most people would likely commit suicide well before they reach their thousandth birthday, not so much out of sadness of any kind, but out of boredom and pointlessness.