"A bastard shall not enter into the congregation of the Lord: even to his tenth generation shall he not enter into the congregation of the Lord". (Deuteronomy 23:2).
jeek takes this to mean that illegitimate children are barred from entering Heaven, but this is not what the text is saying. "Bastards" were, due to the uncleanness of their origins, prohibited from entering into the sanctuary where God was worshipped by the Israelites. Since translation is a tricky business, there is even some dispute as to which illegitimate children were thus excluded: all bastards, or just those whose conception came about because of gross immorality, as in prostitution, adultery, or great licentiousness?

There is no exclusion here from the possibility of salvation. This is but one of a series of purity laws from the Old Testament which apply to joining an earthly congregation, not a heavenly one. While I don't know enough about Judaism to say whether or not this is enforced in Orthodox synagogues, I can say that Christians believe the Law was fulfilled in the person of Jesus Christ, and so this prohibition is not observed.

As a side note, I'd like to add that this would make a bitchin' tattoo.