I am happy to share the addons that I've found useful, however there is a very useful resource for finding addons in the website curse.com. They list the vast majority of addons by category and it is great for helping you determine what might suit your particular needs.
The addons I find most useful include:
- Vuh'Do - as a healing priest, I find this particularly useful, but it is extremely customizable, which can be intimidating to set up. I used Healbot for a long time before finding Vuh'Do. If you only play one class, Healbot might be better for your needs. I happen to play a lot of different toons.
- Gatherer - if you have mining or herbalism, this addon helps you keep track of where you found nodes. It also records nodes that your party/guild members find, giving you a lot more data than you would collect alone.
- Wow-Pro leveling guide. This addon may not be on Curse. However, it is the single most useful tool I've found for getting my leveling toons through the regions efficiently.
- GearScore - I use this for end game purposes, and you are unlikely to need that for some time. It is helpful to me in evaluating who would benefit most from gear that drops in instances, and where the benefits would most likely occur. Probably more sophisticated than you need.
- Recount - If you are healing only, this isn't of much interest to you now either. However, I learned a great deal about how to determine my best DPS rotations when I began using this tool. It reports important information about my party/raid that helps me as a raid leader to know how to use my resources wisely and counsel my teammates.
- Altoholic - As a person who desires to experience the ENTIRE World of Warcraft, I have toons of every class and race, spread across several servers. The only way for me to track which toon has which profession, figure out who is carrying a particular item, and know when I'm scheduled for a raid is to use this tool. It's an absolute MVP for folks with a lot of toons.
- Other addons: I also use Auctioneer to keep track of prices so that I don't throw out things that I should sell, or vendor things that should be auctioned. I use Raid Roll for tracking rolls when distributing loot in raids, and I use Magenuggets for my casters. Many folks I know use some kind of threat meter, but I've found that that game options are acceptable for me in this area.