Currency failure generally occurs due to the type of hyperinflation, and there is always the potential for technical failure, currency competition, political issues and so on. As the main basic rule, there is no currency that can be considered very safe from failure and difficult times. so is it possible that bitcoin can become worthless?
Can banks become worthless? It won't be worthless as long as it has customers. Same answer for Bitcoin's too.
Bitcoin won't be worthless as long as you and me discussing him. Not only us, but there also are a lot of us who supports BTC, so it won't get down, it's a one-way ride where Bitcoin goes forward only.