A Screamer

I suggest reading through the love and logic books. The idea of throwing a tantrum with him is actually completely brilliant, it works every time. They get so freaked out by you acting different than usual that they stop. Love and logic also has some suggestions on time outs, and at least one great idea for tantrums in public. (such as if you expect a tantrum, arrange for a friend to wait outside and call them in to take the child home so that the family can enjoy their outing in peace is very useful).

Your child is stuck in a power struggle with you. He is using disrespect and annoyance as his #1 tool to show you disrespect, because then he gets the attention he wants - your full emotional attention. I'm not implying that he's not getting enough attention. But the attention he is getting may not be fulfulling his emotional needs.

You need to first, show him who's boss with strong, structured discipline. If you'd like my opinion on how, message me privately.
Second, take a hard look at the type of time you are spending with him. Is he watching more than 1 hour of television per day? Is he playing video games? Is he in childcare or babysat most days? When you are spending time with him, what is the focus? Outdoor free play or educational activities like reading books, playing pattycake, building lego toys, etc? When you are busy doing other things is he put in front of the tv to be watched, or is he offered a structured activity in the same rooms as you that he can do on his own? Like coloring, painting, educational worksheets, practicing his alphabet, helping you fold laundry, etc. Think about what activities you can do together that will give him for full attention and he will struggle with power over you less.

Good luck! My boys never went through the terrible 2s - it was the terrible 4s.

If time outs don't stop a behavior in...years, they're not working. As you can see, they are enabling the tantrum habit big time rather than solving it. Kids aren't supposed to cooperate with discipline, they're supposed to avoid it.
Here is some excellent advice on eradicating tantrums and screaming-if you agree with the site, get the book. he does not need to act this way:
www.backtobasicsdiscipline.com

He is getting results, so he continues. I agree with ignoring them. Read the works of Dr. Glenn Latham, a behavioral scientist who applied his studies and research to parenting in a positive, non-punitive way. He has solid methods for changing behavior. Of course, it requires changing your OWN behavior, which is sometimes a bigger challenge! A big part of his methods include very clearly outlining expectations. Make sure he knows EXACTLY what is expected of him. We assume kids always know this and they do not.

Easier said than done, I know... but walk away from him.

If you ask him to do something and he freaks out, walk away and completely ignore him until the tantrum is over. When it's over, remind him of the expectation and make sure that it happens. Don't react to him and please don't try to "rationalize" with him b/c he's simply not listening anyway and you'll find yourself more frustrated.

Also, don't phrase things as questions or end a request with "okay"? My husband and I used to do this all the time and then would get upset when my son would refuse... until we realized that we phrased it as a question. We changed our language and started using more "command" language rather than "request" language- not meanly, just more directly.

"Put your shoes on. It's time to leave for the library." instead of "Do you want to go to the library? Then let's put your shoes on, okay?" Seems minor, but it made life a little easier!

He is trying to control the situation. While you can pick him up keep doing what you need to do so the tantrums can be difused on their own. My son throws tantrums and is three and my parents told me I was big tantrum kid, screaming, crying, clenching fists etc.....Put in a space where he can't get hurt and let it work itself out. Unfortunately when you are in public it is harder to discipline and kids know this. You'll either have to pick him up and carry him to the car or some other non public place and let him go at it. The thing is not to get angry or over react on your part. By the time he is too heavy to carry he should be in a better place and more mature emmotionally.

My pastor's wife just mentioned a book to me that she re-reads occasionally to help her "deal" with one of their children. It's called "The Difficult Child". It is about temperament. You might give it a read. There might be some useful information to help you with your perspective. You don't want to end up disliking your child.. but that can happen if you blame her for her temperament rather than realizing that the behavior results partly from a temperament that she is born with. Some kids are just harder to deal with.
What I scanned through it sounded like a great book~

Neither of my kids ever were "tantrum"ers. She has two who are. She LOVES this book.

http://www.amazon.com/Difficult-Child-Expanded-Revised/dp...

My 4yo has always been a professional tantrum thrower (I even posted a question about his intentional head banging tantrums when he was younger.) He'll throw an all out scream fit but usually doesn't do it in public, not sure if he is too embarrassed or what. Anyhow, at home I usually tell him to let me know when he's done and walk away. If he follows me, which he usually does, still screaming I tell him I can't understand him when he yells and to please talk. That'll usually get him to calm down enough to tell me how mad he is etc. Older he gets the easier he gets.