The Low DPS: These guys can be the hardest to deal with because a lot of the time they're genuinely nice people. Of course, sometimes you get the ones that just won't take your advice out of pride and get very nasty when you point out their mistakes, but most of the time, to me at least, the guys with consistently low DPS aren't jerks. The best way to come at them is politely. First, give them a good inspect and try to see if perhaps their spec is off, or if they're gemming wrong. Ask them if they're hit/exp capped. Find out their rotation. Their low DPS might be because they're stacking the wrong stat, or using the wrong rotation, or simply dying really early in the fight from standing in the goo. Work with them to fix it, especially if they reliably show up to raid.
Sadly, sometimes people are just bad no matter how much you work with them. At this point you have to make the hard decision to bench them or not.
The Whiner: We've probably all been this person once or twice, but a consistent whiner can bring an entire guild's morale down. Whether they bitch about loot, guild rules, raid times, or guild rank, it gets old very fast. Try to nip it in the bud early - whisper them and try to find out what's upsetting them. If the problem can be easily fixed, do it. If they continuously whine, you'll just have to tell them "This is the way things work. It's worked out pretty well for us for awhile, so unless you have a constructive suggestion to change it, please stop whining about it." Either they'll shut up or they won't, and again you'll have to make a decision to bench or guild kick them.
The Bad Attitude: This person is a lot like the whiner, but more aggressive. They might not complain about specific guild things, but more general things like "I'm so bored. I don't want to be here. I could be doing better things right now." Again, send them a whisper and try to find out what the problem is. Give them the benefit of the doubt at first - they might have had a bad day at work/school/etc. If they consistently have a terrible attitude that they're very vocal about, send them a firm message that they need to quit it or there will be consequences. Consequences can include benched for the night up to a guild kick. Decide what's best for your guild.
The Random AFK'er: This guy is really annoying. Pulling trash? AFK. Ready check on boss? AFK. They might even go so far as to mute Vent/Mumble (this has happened to me). Here I say go with the three strike message. The first random AFK let slide, maybe with a mention that they should let you know they're AFKing. The second ask them to warn you before they AFK. The third, give them a firm reprimand, especially if this is all in the same night. After that, start the consequences. A raider that's AFK most of the time is a worthless raider and a person who is always ready would be better to fill the slot.
The Unprepared One: Unprepared means they don't have flasks or buff food (if your guild doesn't provide it), they didn't repair before the raid, or they don't have the proper gear with them if you need them to switch specs. They also might be consistently late to the raid or never bother to try to learn the fights beforehand. They're usually a time sink as you wait for them to log on, or get their gear together, or go repair (if you don't have repair bots), or buy flasks/food/pots. Again, I suggest a three strike system. An unprepared raider is nearly as bad as an AFK one.
The Meter Whore: They spam the DPS or healing meters after every fight, boast about their position on the charts even for trash pulls, and constantly put down other raiders. Their ego is bigger than your entire raid put together. The problem with these guys is they love topping the meters so much, they're more likely to tunnel vision and make a mistake and get themselves killed.
Back in ICC, we were working on Rotface, we had a pally healer who was pretty damn good. He thought he was godly though. He got the debuff, ran out, stopped, healed the tank, died. We asked him why he didn't cleanse and run - his response was if he stopped healing the tanks they would die since he was carrying the heals. He really thought he was the sole reason the tanks were alive. /sigh
Meter whores are another one that's hard to deal with because they do tend to be exemplary players. However, constant meter spamming and putting down other players will also lower guild morale. If you see other players getting frustrated and fed up with the meter whore, politely but firmly tell them to stop the bragging. If they refuse, start the consequences.
--------------------------------------------------------In conclusion, should you give a problem raider an ultimatum?
Eventually, yes. What the ultimatum is depends on the what type of raider they are and what works for your guild.