There has of late been quite a lot of reference to Pelagianism in the Church and elsewhere, particularly in the context of recent papal teaching, and it is interesting to reflect on why it is heretical, and what its implications may be.
I do not intend to reproduce a great deal of Bones' excellent post, but would like to add a few thoughts.
Pelagius (incidentally a native of Britain, so my Catholic Dictionary tells me) rejected the doctrine of Original Sin, and denied the necessity of grace for salvation. Essentially, he taught that it was possible to be 'good without God', and to achieve Heaven without the need for Him, essentially overstating the doctrine of Free Will. This was condemned by the Council of Carthage, whose decision was later ratified by the pope (an early example of the use of Infallibility?), causing St. Augustine to utter his famous words 'Roma locuta est, causa finita est' - 'Rome has spoken, the case is ended.'
What Bones has picked up is that we see a great deal of this attitude in our present-day society. Among Christians there is often an emphasis on works, particularly of a social or environmental kind, at the expense of worship and religious devotion. The liturgy has in some cases become a social event, with emphasis on human intereactions rather than contemplation of the divine (an example must be the baseball-capped ministers at WYD in Rio dispensing Our Lord's Precious Blood in a plastic cup, like cheap booze at a party - but I digress - end of rant).
There also seems to be lots of emphasis on, for example 'good atheists', ie atheists who live virtuous and moral lives - but then who decides what is good and moral? We need an external reference point to tell us what we ought to do, and this is, of course, God. It is, of course, easy not to recognise His influence - one of the consequences of omnipresence, just as we do not usually notice the air around us because it's always there.
The danger with trying to do good without reference to God is that we tend to focus on trying to be nice to people, rather than truly loving our neighbour and wanting the best for them, which is ultimately that their soul gets to Heaven (other options are not, I hope, something you would wish on anyone). Sadly, without divine guidance and support, this can lead to, for example, tolerating, or even encouraging immorality in a misguided effort to achieve 'equality' or avoid 'discrimination'. There are very few of us who would be deliberately evil, but very many, if not all, of us sin through a distortion of the good, which is the devil's favourite trick.
Let us remember, then, that we cannot 'go it alone', or as Blessed Teresa of Calcutta once said 'I'm not OK, and you're not OK, and that's why we need Jesus.' ... and that is why Pelagianism is a heresy.