Voyager is moving at \~17KPS ... divided into 300,000 KPS ... multiplied by 3600 * 24 * 365.25 ... multiplied by 20. \~370,000 years to reach Gliese. To me, a 200-year mission is about what I could imagine our civilization buying into. No way gravity assist can scale; I don't think solar sails scale; no way we're putting enough nuclear bombs into space to do an Orion thing. Lessee... Wikipedia says ion drives have exhaust speeds of \~30KPS ... And this Wikipedia article seems wildly optimistic about "technologies requiring further research" ... Some kind of electromagnetic mass-driver I can imagine (but then, my brother-in-law works at Fermilab, so I'm biased) ...
Update: Surely (?) Dan Ciruli is correct in his comments that without friction, you can go much faster than your exhaust ... So let's say ion drive ... Lessee ... 10\^-4 g ... d = 1/2 at\^2 ... turnaround at 10 light years ... \~620 years with a peak velocity of 9000 km/sec ... now we're talking ... get a little more acceleration and we're on that planet like locusts on a cornfield.