There are corporations and alliances who live and die by standings. Diplomacy around standings is a big thing for them. I know of some organisations who set their rules of engagement based on them. This is a strange policy to some and the norm for others. Some even sell standings, again, an alien concept.
Excellent Standing +10
'Blues'. Reserved for member alts and member alt corps only. I have never set anybody other than alts blue before and hopefully never will. Some people are known to set their friends blue, personally I'd rather shoot my friends in the face and then shake hands afterwards.
Good Standing +5
'Light-blues'. Rarely if ever used, especially at corporate level. On rare occasions an outside service might be set light-blue to enable ease of incoming goods, such as a jump freighter courier service for example. If the cynos are being shot the goods won't get delivered on time and in some cases not at all, so a light-blue standing is essential in these situations or members won't get to play with their new toys.
I will use this standing setting on occasions with an attached note with information on the pilot in question. For example, if I spot a two-month old character wandering around low-sec in a navy battleship and I am not in a position to take him down there and then or he goes back behind the high-sec fence. In this situation I will set him neutral and add to the address book, then if I spot him again in local at a later date I will know he is on my target watch list. Similarly, I will use this standing to add known stab-monkeys, plex-cloakers or smack-talkers to my list. This standing setting is basically a list of people I want to kill. I find setting them neutral helps in my extermination plans.
Bad Standing -5
'Oranges'. This standing setting is very much a misnomer. I set people and corporations/alliances orange if I like them, if they're good dudes and known for bringing good fights. An example would be a rival pirate corporation who might live in the same area who doesn't ship up or bring ECM to a 1v1 frig fight. We might sometimes share a fleet or spend the day shooting each other, but they're certainly not 'bad' as the name would suggest.
Terrible Standing -10
'Reds'. Reserved for the extremely bad people of eve. Anti-pirate corporations would be set red. Insta-lock gate campers or blobbers or known ECM abusers would be set red. Booster alts are always set red, as too are known scout alts or Falcon alts. Spotting a bunch of reds in local should give an inclination that you're probably not going to get that good fight you crave. By far my most abused standing setting, my list of reds is extremely clogged, such is the nature of the beast.
So how do you use standings?