Deadly Boss Mods (DBM)- DBM helps you out by announcing various boss mechanics. This can include warnings to move or timers for various mechanics. DBM will sometimes audibly count down to events which helps the raider move before they take a lot of damage or before an event. It will also announce spells and debuffs cast and changes of phases. DBM also works for instances and battlegrounds.
GTFO - GTFO is a great addon in addition to DBM. GTFO will make a sound if you are standing in something on the ground, get hit by something your not suppose to, or generally dying in some way. It is nice because you will hear the sound and know you have to move out of something even if you are focused on healing or rotation. Another perk of the addon is that it warns you of things outside of raiding also like getting fatigue or drowning.
Recount - This addon keeps track of DPS, Healing, Interrupts, CC breaks, and a handful of other stats. This addon isn't something mandatory to raid but it does help keep track of the dps or healing you are doing in relation to others in your raid. You can click on each member and see what spells they were using to do damage and heals and you can in turn use that to help figure out your own rotation. You can also see the main mobs the person is DPSing or healing. This can be very useful if certain members are not changing targets during a fight.
Omen Threat Meter - Omen is an addon all raiders should have. It shows how much threat you have on a mob. This is extremely important for tanks and DPS. If the DPS sees they are getting too close to the tanks threat they can stop DPSing until their threat goes down or can Misdirect or Tricks of the Trade threat to the tank.
Healbot or Vuhdo - Both of these addons deal with healing and decursing. You don't use both. Choose one or the other. Quite a few people prefer Healbot but test out both if you haven't used them before. You can set up your healing spells and cleansing spells to mouse buttons and shift/ctrl/alt modifiers. Instead of having to click on each person to heal them you just click on the addons raiding frames to directly heal them. Using one of these addons is much more efficient and easier to heal than manually clicking a raid member then clicking the healing spell you want. You can also see debuffs on all players, a quick view of everyone's health, and which players have died.
Omni CC- This addon changes the count downs of your buttons. Instead of seeing a clock dial counting down your buttons you see a number. Instead of having to guess how much time you have before a button can be hit you can just look at the number and know if you have time to hit another spell before the cooldown is up.
Tidy Plates - This addon was made for tanks but it has expanded to be helpful to all classes. It adds a health plate above a mobs head. You can change the style depending on what info you want to see. If you are a rogue you can have it show the timers of your bleeds and poisons. If you are a tank you can show the mobs you have a lot of threat on and which ones you are losing threat. DPS and heals can see if they are getting too much argo on certain mobs. The plates can change color depending on how much threat you have on a mob and also if there are any raid markers on the mob. The plate will change to a certain color marker such as white for skull, red for X, and yellow for diamond.
Rating Buster - Sometimes when looking at gear that dropped it is hard to decide which is better, what you are wearing or what dropped. This addon helps with showing how your stats will change. It takes into account your class and spec. You can see what stats you lose and what you gain. It also shows resilience, mana, armor, and health changes.