In the past, I've suggested more fluid, not-so-binary alignments, in the style of Pendragon's trait pairs, but with just two pairs: Lawful/Chaotic and Good/Evil.
In Pendragon, each pair sums to 20 (e.g., Chaste 15/Lustful 5) -- it's a d20 roll-under system -- but we could just as easily have them sum to 0 (e.g., Good +5/Evil -5) for D&D, to roll against a DC of 10 (or 11, if you're finicky).
A more complicated but, perhaps, more interesting option, at least for Pendragon fans, is to stick to Pendragon's 13 trait pairs and use its concept of virtues, with five virtues for each religion.
For instance, the 13 trait pairs in Pendragon are:
Chaste / Lustful
Energetic / Lazy
Forgiving / Vengeful
Generous / Selfish
Honest / Deceitful
Just / Arbitrary
Merciful / Cruel
Modest / Proud
Pious / Worldly
Prudent / Reckless
Temperate / Indulgent
Trusting / Suspicious
Valorous / Cowardly
The five virtues for Christians (in Pendragon) are: Chaste, Modest, Forgiving, Merciful, and Temperate. If all five of those virtues are 16 or higher, the character gets a Christian bonus of +6 hit points (in Pendragon). A D&D campaign could easily require those virtues of Clerics of Pelor.
Pendragon also has a notion of Chivalrous traits irrespective of religion: Energetic, Generous, Just, Merciful, Modest, and Valorous. A Paladin coud be expected to keep those traits at 16 or higher (or sum 80 or higher, as in Pendragon).
Societies could grant the equivalent of Honor to individuals who meet their virtue requirements. For instance, in Orc society, warriors who are sufficiently Valorous, Suspicious, Indulgent, Reckless, Worldly, Proud, etc. might gain respect and power.
Or we could work our way back to D&D's alignments, but a bit more roundabout. We could divvy up Pendragon's 13 trait pairs into two mega-trait pairs: Lawful/Chaotic and Good/Evil.
Lawful/Chaotic
Chaste/Lustful
Energetic/Lazy
Just/Arbitrary
Modest/Proud
Pious/Worldly
Prudent/Reckless
Temperate/Indulgent
Good/Evil
Forgiving/Vengeful
Generous/Selfish
Merciful/Cruel
Honest/Deceitful
Trusting/Suspicious
Valorous/Cowardly
The individual traits are much more clearly defined than something like "Chaotic", but we can still work back to the D&D alignments if we want them.