I thought I would post a thread to point some people who are a little unfamiliar with add-ons in a general good direction to start.
This is all my own personal opinion, so bear with me.
MUST HAVES:
Deadly Boss Mods
Omen Threat Meter
TomTom***
Lightheaded***
***a word about these two, TomTom is a Waypoint arrow like GPS for questing. Light-headed, links your quest log to Wowhead, so all the tips we normally alt-tab to surf the web for are available without minimizing the game and surfing the internet, including the mob locations, tips and strategies for any given quest.
WowMatrix- get this one first...It manages all your add-ons, including installation, uninstallation and updates.
MiniMap Button- Puts all of your addons into one button on your mini map
OneBag- Allows you to view all your bags as one large bag. There is also OneBank, which does the same thing for your bank bags.
MACROS
If anyone needs help with macros, I will help point you to some good resources. I am a macro fanatic when it comes to raiding and playing in general (macros have saved my healer many times while I was tanking...I have a mouse-over macro that will charge, bash and growl at a target just by putting my cursor over a target that is heading for my healer and hitting a hot key).
Thats all I can really think of to get you started. If anyone can think of anything I missed, or has add-ons they REALLY like, feel free to reply.

Great post Dark! I've been meaning to put together a post about recommended add ons, but I have not had enough time recently. There are a few I would like to add to this list.

Quartz:

This is a very small add-on that keeps surprising me with how useful it is. Nominally this is just a cast bar add-on that lets you move your cast bar wherever you want it to be. However, it also lets you place your target's cast bar wherever you want it to be, so you can always see as soon as they beginning casting their spells so you can be ready with an interrupt. It also shows you when you can start casting your next spell (which is never as soon as you first one is done. Thanks to latency, you can actually queue your next spell before your first one is done and increase your dps/healing). Finally it also comes with a debuff tracker. It will show each of the debuffs you have on your target, and how long they will last (or if targeting a friendly character, it will show the buffs you have put on them and how long they will last). I cannot recommend this highly enough.

As mentioned above, Omen and Deadly Boss Mods are both incredibly useful and required for raiding with Serendipity.

For healers, I have heard great things about mods such as Healbot/Grid/Clique, but I have never used them myself to see how they stack up.

There are a variety of add-ons out there that allow you to minimize how much space your UI takes up, and see more of what is happening at any given moment. I use mods such as Domino (action bar mod), X-Perl (Unit Frames), and Mapster (Map mod) to name a few just to maximize the amount of game that I can see.

Finally, if you are a paladin or raid leader, you should consider investing in PallyPower, because it allows you to coordinate blessings very easily, and see when they go down. However, it only works if all the paladins in the raid have it. Seeing as how I am the only paladin right now, it should not be a problem, though .

Hope this helps somewhat.

I use Macaroon to mod my UI with a few other plug-ins. It DOES make a big difference having more screen area when you raid. The learning curve was a little steep on Macaroon for me because I was so used to Trinity Bars (and Bartender before that). I did some pretty stupid things with it (like going through almost a whole instance before I could roll on anything because my loot bars were gone!!!).

Trinity was the BEST! It's a shame they quit updating it.
I also use Domino, never could get Macaroon to work right for me.
I may have to try it again and maybe with some help from Darkallanon on vent I can get it working right. They say it is pretty compariable to Trinity.

It is, once you figure out the quirks. It's just not as user friendly, but once you figure it out you can do anything you could do with Trinity.

A few other addons that most people would find useful:

OmniCC: This is an addon that works with essentially any action bar addon to replace the clock like cooldown timer on your skills with actual numbers. I have found I can no longer play without this addon. Judging when longer cooldowns (like trinkets, Divine Shield, Lay on Hands, etc) are up without it becomes an exercise in trying to determine if a thin black line is there or not. Something I try and avoid during raid fights . It also takes up next to no memory so there is really no downside to downloading this.

RatingsBuster: This converts all those annoying ratings into much easier to understand percentages. It also tells you what bonuses (crit rating, ap, etc) you will get from stats. Finally, it will also offer you a quick, concise summary of how your stats will change when you are changing a piece of equipment, with stats you are losing in red, and stats you are gaining in green. Makes deciding upgrades slightly easier. (My version does not take enchants into account currently, but that is probably just a bug).

Recount: This is a dps meter, and not strictly required (and in many cases it may be detrimental as it is a memory hog). However, if you are looking to improve your game, downloading this addon and practicing your dps rotation on the appropriate dummy can give you a good idea of what you need to work on. It will offer breakdowns of your skill usage, miss/crit %'s, where your damage is coming from, and most importantly, your overall dps numbers. Again, it takes up a lot of memory so you may want to disable it for a raid, but it is very handy in improving your damage.

Nice. I will have to try RatingsBuster. It sounds like an in-game version of the sanbox on Warcrafter.net....if you haven't used that site, I highly recommend it. You can craft your character with any item in the game including enchants and gems and then select build stats, and it will show you what your stats will be after you obtain and equip said item.