This system was orignally designed by Andreas and over time given a few tweaks.
How much a character likes or dislikes another character is based on a number of factors, such as race, alignment, beliefs, interests and how much time they have spent with the character. These are the initial factors that are used to calculate the type and intensity of feelings a character may have for another.
To calculate how friendly or otherwise two characters are likely to feel towards each other:
Race: use the table in Unearthed Arcana (p.12). P = +3, G = +2, T = +1, N = 0, A = -1, H = -3. Note that some characters may like somebody less than they are liked in return, or vice-versa, e.g. half-elves tend to like elves more than the elves like half-elves, some kind of blood snobbery going on here.
Alignment: for each similar alignment (e.g. both characters are chaotic, or both are good) add 1. For each opposite alignment (e.g. law/chaos, good/evil) subtract 2. Character of true neutral alignment and characters of extreme alignments, i.e. LG, CG, LE, CE, are considered -1 to each other.
Beliefs: characters worshipping the same deity gain +3, worshipping a favoured deity of the same mythology gains +2, worshipping a deity of the same mythology gains +1 unless the deity is an enemy of the character’s deity in which case minuses will apply. Characters who worship deities from different mythologies but that have the same spheres of influence, e.g. hunting or fertility or storms, gain a +1 or +2.
Interests: if characters have a strong interest that is outside the normal scope of an adventurer’s agenda, such as a second skill, knowledge and/or special interest in a subject, or similar experiences in their past they may have a +1 or +2 to their interaction.
Time: for every two adventures or so that a character completes with another character, they gain +1 as they enjoy each other’s company and learn to trust each other more and more (learn to tolerate the worst excesses of their appalling irritations and annoyances).
Events: every so often something may happen suddenly to alter the way a character feels about another, e.g. saving their life, cutting off one of their limbs, helping them out in some big way, shagging their wife, committing some deed of great benevolence or malice as perceived by the character, etc. These events are likely to shift the way these characters feel about each other and so alter their interaction score. If a character feels they have been glorified, slighted, delighted, humiliated (etc.) to the extent that they wish to alter their interaction score with the offending/wonderful character, the DM should be informed at once.
What the Scores Mean
+5 is absolutely the best of friends, -5 shows a deep and relentless loathing, with numbers in between showing the varying degrees of warmth or frostiness.
Characters with interaction scores of -10 or below are likely to seek each other out to kill their enemy.
Scores in excess of +5 doesn’t necessarily mean the characters are intimately acquainted with each other’s most secret places (although this is certainly not beyond the realms of possibility), rather it means that the bonds of trust and friendship they share can be strained a few times by the odd misdemeanor or mistake before it starts to take any serious toll.