I do think that Star Trek will still be around in 150 years. I think it'll come and go, have periods of popularity and decline, but ultimately will be reinvented/rebooted time and time again for different generations of audiences. In 150 years, though, it'll probably be totally unrecognizable to us
with perhaps only the Enterprise
, Kirk, and Spock being the only things retained from the original with the rest being long-since altered or revisioned, IMO.
By then, it'll probably be transmitted on demand directly into people's brains...