I made this table for my Galbaruc campaign, though with some tweaking it might work for yours. I jotted down 106 entries, but ended up scrapping a lot of them, narrowing it down to the 50 I liked best. My campaign only has 2 PC races in it (Humans and Vat-Spawn) so this table's for Human characters, to give them a little distinction.
These are probably not even remotely balanced.
| d100 | Peculiarity | 
| 1-2 | You are Androgynous:  +4 to attempts to pass as a (nonspecific)   member of the opposite sex.   | 
| 3-4 | You are a Libertine:   You must make a successful WIS roll to avoid Carousing if you finish an   expedition with more loot than you started out with. | 
| 5-6 | You are a Struldbrug.  You have immortality (barring death by   violence, drowning, etc.) without eternal youth. | 
| 7-8 | For some reason, (1-2) dogs (3-4) cats (5-6) birds   hate you.  They’ll growl/hiss/squawk at   your approach, and the GM rolls 2d6 each round you remain within 10 ft. of   the animals in question, which attack on a roll of 2 even numbers. | 
| 9-10 | You have a Doppelganger.  This individual is identical to you in   appearance and stats, and wholeheartedly devoted to your ruin and   destruction.  It will refrain from   outright killing you until it feels that the you’ve undergone sufficient   discomfort, loss, and humiliation. | 
| 11-12 | You are a shape-shifting   reptile from another plane of existence.     Your true from is undetectable by mundane means, but if it is ever   compromised, you will need to devour another human to take their shape, a   process requiring 48 hours in undisturbed darkness.  Your ancient enemies the (1-2) red (3-4)   black scaled reptiles have their agents as well, and you will periodically receive   orders from your superiors as you carry on the millennia-long struggle   against your rivals,. | 
| 13-14 | You may perceive oracular significance in the buzzing of insects. | 
| 15-16 | Some years ago, you were a member of a secret cult.  Despite certain dire oaths to the contrary,   you abandoned it.  Your former brothers   and sisters are always on the lookout for the runaway.  Gain   Distinctive Tattoo. | 
| 17-18 | You are extraordinarily   forgettable.  This can be   frustrating, as you must constantly remind casual acquaintances of your   identity, but it comes in handy when eyewitnesses to the robbery are   describing suspects to the authorities. | 
| 19-20 | You are a Gourmand.  You must make a Save vs. Spell roll at +4   difficulty to turn down the chance of experiencing a new taste. | 
| 21-22 | Once per session, you may summon the spirit of an illustrious dead ancestor of yours   for five minutes of consultation.  | 
| 23-24 | A powerful   Magic-User , for some unknown reason, has taken an interest in your progress,   and will act behind the scenes as a patron.  This assistance will not come without a   price. | 
| 25-26 | You were born   with a tail.  Casual investigation   has led you to believe that everyone is, and that there is a secret   conspiracy of physicians and midwives to lop them off at birth, to some unguessable   purpose. | 
| 27-28 | You were   born with a birth caul: While it remains on your person, you cannot   drown. | 
| 29-30 | You were baptized   in the blood of the Salamander.    You take no damage from fire. | 
| 31-32 | You are a musical   prodigy.  You may give an   unforgettable performance on any instrument, but the instrument will   disintegrate or fall apart in dramatic fashion as soon as you finish playing. | 
| 33-34 | True or not, you   have a reputation as a colossal pervert – a sexual adventurer of the most   depraved kind.  This will be met with   interest and enthusiasm in some quarters, and suspicion and hostility in   others. | 
| 35-36 | You bear an executioner’s   brand on your thumb, indicating a reprieve from the death penalty.  If found guilty for any crime in the   future, you will swing for it. | 
| 37-38 | You are an ordained   cleric in the religion of your choice.    You possess no mystic powers, but can perform all observances,   rituals, and ceremonies expected of you.    You have not been officially defrocked, but any relationship with the   church hierarchy is strained, at best.     Reroll if you’re already playing a “capital C” Cleric. | 
| 39-40 | Ghosts, specters,   etc. are especially drawn to you.    These visitations are not always malevolent, and often take the form   of pleas for aid and redress of past wrongs.  | 
| 41-42 | An otherworldly   Insect parasite has lodged itself in the base of your spine.  You will occasionally experience strange   fascinations and cravings, which you may attempt to resist with a Save vs. Spell. | 
| 43-44 | You are an albino. | 
| 45-46 | You are unable   to grow any hair.  No eyebrows, no   pubes, nothin’.   You are blessed to   live in a time and place when wigs are fashionable. | 
| 47-48 | You have a coin   with the sigil of a Minor Demon carved into it.  You may summon this demon once to fulfill a   favor, after which, the demon returns to its own plane and the coin is   reduced to a worthless blackened lump of slag. | 
| 49-50 | You’ve woken   up from suspended animation  after   d10 x100 years.  Take 1 dot in Lore,   but your knowledge may be somewhat out of date.  Your speech will probably sound a bit   archaic, as well. | 
| 51-52 | Every time you fail your Save while Carousing,  make another Save (vs. Magic).  If you fail, you dream a monster into existence.  You (or the GM) roll up a monster using a   random generator, which then blinks into existence, terrorizing the town or   countryside and working its way toward you. | 
| 53-54 | You have a horrible,   rasping speaking voice but can sing like an angel. | 
| 55-56 | You can hold   your liquor like a champ.  +4 to   save vs. poison when boozing it up. | 
| 57-58 | You have an inch-tall horn spiraling out of your   forehead. | 
| 59-60 | Your   physical body is the chain that keeps a monster imprisoned.   The GM will secretly roll a number on a   d100.  When you’ve taken that much HP damage,   (or die) the creature breaks its bonds and escapes.  Magical Healing can reverse the process,   but only at a rate of 1 HP/instance. | 
| 61-62 | Someone believes you to be the reincarnation of their former lover from a past life. | 
| 63-64 | There is a 15%   chance of switching bodies with one’s companion during sex. (particularly   abandoned libertines may need to roll again to narrow it down).  You cannot re-enter (as it were) the same   body after leaving it. | 
| 65-66 | You have a   lofty hereditary title to a place that doesn’t technically exist anymore | 
| 67-68 | Attention   whore: +1 to all rolls when in front of at least one non-participant  that’s paying attention. | 
| 69-70 | You are a Compulsive   gambler : Save vs. Spell to avoid participating in games of chance. | 
| 71-72 | You were born during a thunderstorm beneath a   blasted tree--  take no damage from lighting/electricity. | 
| 73-74 | Through the use of drugs, ecstatic ritual, etc., you can enter a Berserk state.  +4 to hit, damage explodes on the highest 3   digits (melee) for d10 + CON modifier rounds, at the end of which, you fall unconscious   for d6 rounds.  While Berserk you must make   a Save vs. Spell to avoid attacking allies within 15 ft. of you. | 
| 75-76 | You are the deposed   Heir to an Island Prince.  Some   day, you will raise an army and take back what is rightfully yours! | 
| 77-78 | Your teeth   have been filed to points. | 
| 79-80 | You are a Eunuch,   with all that implies.  Roll again if   female. | 
| 81-82 | You have some training as an Actor – +2 bonus to pretend to be of higher/lower social status. | 
| 83-84 | You have a cheap tin talisman of Seppophis the Huntress.  +2 to attempts to find an individual.  Your pursuers have a -2 to find you. | 
| 85-86 | You have in your possession a  small   shard from one of the mysterious standing stones that litter the   surrounding countryside. | 
| 87-88 | You have no   fingernails on your left hand. | 
| 89-90 | Your weapon   is an ancient, storied implement of great renown and prestige.  Generations of proud warriors have wielded it   with glory and distinction.  It even   has a name.  So your mother always   insisted, and so you will tell the pawnbroker when you run out of money for   gin. | 
| 91-92 | You are Double   jointed.  This has all kinds of fun   mechanics implications that can surely be dealt with on an ad hoc basis.  | 
| 93-94 | Keith Richards:   take a +4 bonus and R2K1 on all Saves vs. Poison when taking drugs. | 
| 95-96 | You have a Holy   guardian angel and it loathes you | 
| 97-98 | Pugilist!  Your fists do d4 damage, R2K1. | 
| 99-100 | You have a pickled   punk – a tiny, two-headed fetus in a jar.    It can tell you one fact about an individual for each drop of their   blood you put in its brine.  After 12   drops, the brine will be completely clouded with blood and the unfortunate creature   will finally die. | 
 

 
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