I've always ran with a standard set of addons, but I'm curious to see if you guys think there are any addons (outside of what I use) that you would view as more of a requirement for raiding. What type of information is needed to be seen?
Both to compare vs. my current setup that I'm running, and for my prospects of a friend and I taking over as a raid leader(s) for my guild.
I'm not going to share the list of addons I currently use so nothing goes unmentioned simply because OP already uses it.
Required for raiding? DBM or BigWigs, since the Blizzard designers assume that serious raid teams use them. You could depend on others to cue you, or whatever, but you are gimping your performance compared to what the fight designers expect you to be able to do. (Hint: they deliberately make it hard or impossible to timer some things in the fights as a consequence of this assumption, so what is timered is a deliberate decision on their part, not just random.)
Also, install one, then turn off every notification it has unless you know exactly what your reaction to it is -- the specific, active thing you do in response to that information. Only turn back on notifications if you have a specific action you need to take, and are not getting told about it. Don't use the defaults, or leave everything on.
Required as a raid leader: just that. Beyond that, you don't strictly need anything more, and you can do fine. However, as Treken notes, "Death Note" is very useful, or some other tool that will show you what happened in the 30 seconds or minute before someone died can avoid having to ask why someone died that fourth time -- now you *know* it was to the same mechanic. Skada and Recount offer the same service, but IMO they are inferior to Death Note in terms of readability.
It can be helpful to have a combat log addon that will show you who damaged which mobs, or where damage landed from players, so you can see if that raider switched to the desecrated weapon like they were supposed to, or they just tunnelled the boss. Again, doesn't necessarily tell you why, but can point you in the direction of solving problems.
If you are the loot master, get an addon. "Raid Roll with EPGP" is good if you either roll for loot, or use EPGP; similar addons exist for other loot distribution schemes. These usually automate the announcement, figuring out the winner, and assigning the loot. They can eliminate one of the biggest sources of annoyance, human error, from the loot master position.
Fatality or some other death announcer, and Ensidia Fails, can be useful if you want to abuse your raiders in chat, automatically, when they do something wrong or get unlucky. Actual value will vary based on your team and approach; personally, I found the former useless, but have private notifications for tank and healer deaths, and the later very helpful but *only* when sent to me privately, so I could interpret it and talk to someone by voice.
Raid Buff Status (RBS) is really helpful. It tracks all the things that people should be doing (eg: flasks, presences, buffs, etc), and lets you see if they need to fix something. Don't use the "whisper / announce what needs doing" feature without negotiating with your team, but if they agree you have a one-button tool to request specific people buff up, removing the delay while those four paladins work out that none of the others have hit the button yet.
If you pug a lot, or use a rotating roster, there are a couple of addons that show you what buffs you have covered in the team, so that you can figure out what you still need to fill out the buff list. Just browse curse if that sounds useful to you.
Finally, I would recommend something that allows you to add custom events to things. WeakAuras is always popular, as is TellMeWhen, but other tools such as Boss Notes can deliver the same thing. Basically, "when this happens, do this thing", which allows you to add reminders for those things you need to know.