From what I've picked up so far:
Vultures were the most sacred birds because they never killed a living thing (hence the Romulus and Remus competition as to who would see the most vultures would be the founder of the city); Geece were sacred and saved Rome (As they warned the Romans that the Gauls were trying to take their citadel durring their sack of Rome); the chickens eating as mentioned before (the hungrier they were the better).
The livers of certain animals were considered to predict a positive outcome if they were clear during their inspection and if they contained a defined 'head' (but if the head was missing this was bad), lightening striking a temple usually indicated that the said God was unsatisified whereas lightening striking a wall indicated the same (as far as I can tell anyways, probably whichever God was considered the patron of said city was the one who was angry); derformed animals and people at birth (having both sexual organs particularly) were considered abombinations and cast into the sea; 'raining stones' (not hail as I orginally thought since this is mentioned seperately) was an omen of particular concern and the books were always pulled out when that happend.
Other then those, there are many, many mentions of isolated incidences such as strange lights and objects in the sky, statures bleeding or sweating, the sun turning red, rivers and fountains issuing blood, etc...