Hmm, for this to be such a widely held belief, I'm not getting nearly as much scriptural evidence as I expected. I'm a little surprised by that.
There is much scripture for it, also many illistations and much allusion to it in scripture.
Such passages as already are given (like rbell has given) as irrefutable, especially when one holds to context. It is appointed unto man, once to die and them the judgment. IOW - all men will die and all men will be judged. And thus the only way to not be condemned in judgement is to receive the only means provided to escape eternal punishment/damnation - also explained as perishing which is contrasted negitively with life. one such example is Jude 7 and 12-13.
There are various aspects to this eternal shared by all therein, such as darkness, fire, worms that do not die, sorrow, without hope, ect..
We see this judgment in many places of scripture such as John 3:16-17 - speaking of why Jesus came to earth. We read in Rom 3:25 that what Christ did is NOT automatically applied to ANY person unless they receive it by faith and that, in Him alone.
Rev 20:10-15 (and others) speak of the Great white throne Judgment in which there is no second chance to repent (of which the passage speaking once to die - does as well) but the judgment. And all THESE people are judged according to their works, and the 'type' of judgment upon their works is determined by whether or not they are found written in the book of life.
Scripture also tells us that Judgment is without mercy. We see this in many passages and illistrations (ie. Lazarus and rich man, marriage feast, good and evil servants..) According to scripture there is a resurrection to life )the coming of Christ Jesus) and a resurrection to damnation (Rev 20). Also Mat 18:8 speaks to the fact of being condemned of living - when we die. Mat 25:36 states the same thing - that when we die we will either go to life or death - and in ALL places find our salvation is dependant entirely upon our faith in Him and His finished work (again Rom 3:25).
There are passages in scripture which speak to the fact that men, while still alive, are given over to their sins because God knows they have come to a point where they will not believe (Rom 1:18-
32; 2 Thes 2:10-12; Prov 1:22-33; and many others)
There is much much more, so to me I am not only baffled but mystified why you make the assumption there isn't much scripture on it since a great deal of the scriptures speak both to and of it. With the amount there is I am makeing the assumption you have really looked this up to study it out though. - this is just an assumption
If the above is not true then what is the point of the gospel. Scripture states emphatically - believe and be saved NOT you are saved therefore you will believe. Otherwise Jesus Himself is a liar (John 5:24) and thus is not the Messiah promised, our salvation fortold, nor our God made flesh and dwelling amoung us.
If you need more or would more examples or explaination, just ask.