There are many who would say that the Great Commission was for the generation of the original recipients only. Others say that it is trans-generational and applies to all belivers for all time. Which is more accurate and why?
I would say that we have to consider that the Great Commission is trans-generational. In the first place, Jesus' commission to His disciples included, "teaching them to observe all things that I have commanded you..." (Matt. 28:20); surely "go and make disciples of all the nations" (v. 19) should be included in the "all things" He commanded them, shouldn't it?
Secondly, we must consider the scope of the great commission which was, "to the end of the earth." (Acts 1:8) This was not accomplished in the Apostle's lifetime - indeed, there is still much work to do even today.
Finally, if this command was not trans-generational, then what about everything else that Jesus taught and commanded? Was it all just for the hearers of that generation? And if not, how can we know the difference? There would have to be some compelling evidence for us not to consider any Biblical command, and especially a command from Jesus Himself, as trans-generational. Of the Old Testament Paul wrote, "whatever things were written before were written for our learning" (Rom. 15:4), and "all these things happened to them as examples, and were written for our admonition" (1 Cor. 10:11-12), and again "All Scripture is given by inspiration of God and is profitable" (2 Tim. 3:16-17). How could this be true of the Old Testament and not be true of the Gospels?
I have heard the 1st arguement many times, and I agree with it. Some do not.
Secondly, I find it interesting that you couple Acts 1:8 with the Great Commission. Most would consider them separate. Different in scope, to different groups of people, with different agendas. I don't know how we can biblically join them, but I would be interested in any ideas.
Thirdly, some would say that according to Colossians 1:6 "which has come to you, as indeed in the whole world it is bearing fruit and growing—as it also does among you, since the day you heard it and understood the grace of God in truth," that the Gospel has gone out to the whole world. (I find it a bit weak)
Re: Coupling Acts 1:8 and Matt. 28:19 - I would also include Mark 16:15 as part of the great commission as well. Matthew, Mark and Luke each record a commission and each one is different according to their different purposes in wiriting. But all of them were writing 30 or so years after the events happened and, to my mind, they were writing to exhort their readers to get out and get the work done, not to report a past historical event. Whether you see these as three separate commissions, or slightly different aspects of the same commission is immaterial; to my mind they are all still applicable to us today.
Re: Col. 1:6 - I also find this argument extremely weak. Even if Paul had intended to communicate that there was no one left to hear the gospel - which I highly doubt - he says nothing there about discontinuing the work. In fact, writing some time later, in 2 Timothy 4, he commands Timothy to "Preach the Word!" (v. 2) and "Do the work of an evangelist" (v. 5) It sounds to me like he wanted Timothy to continue the work...