[SoothingDave]

Is it still the case that they should not receive communion? My father's marriage to my mother has never been annulled, yet he and his new wife joined a parish, and receive communion every week.

If the first marriage was not annulled, then he is still married to your mother. In which case his "new wife" is not his wife at all.

That's called "adultery," and people engaged in it are in a state of mortal sin. Taking communion in a state of sin is forbidden.

SD

[eastsider]

[P]eople engaged in it are in a state of mortal sin.

Objectively, yes.

[AdA$tra]

That's called "adultery,"

Not very "soothing" Dave...LOL.

[plain talk]

Taking communion in a state of sin is forbidden.

I guess you meant unrependent sin, didn't you? We are all in a state of sin.

[capitan_refugio]

From the question, you may not have all the facts.

Was the first marriage in the church?
Was it a "mixed-faith" marriage?
Had each been baptised?
Did one or the other renounce their faith?
Is one a member of the Kennedy family? ;^)

[Knither]

However, there is the principle of "primacy of conscience" which basically says that "judging the sinfulness of any particular act is a matter ultimately between God and the individual person. This is the function of one’s conscience, which the Second Vatican Council described as the divine voice echoing in our depths, as a law written by God in human hearts. A person must always obey the certain judgment of his or her conscience."
A bishop can ask that a particular person stop doing something which gives scandal, as he has done in the case of Daschle, but many remarried Catholics who are somewhere in the process of getting an official annulment have decided that God knows the first marriage was not valid, and that it is better to fully participate in worship and communion than to wait for the slow process of the Church's marriage tribunal.