Healbot is very nice for healing (funny that!) but another quite useful tool is Grid (and its addon modules). This is highly configurable and aims to fit as much information as it can in a small area but without it being hard to read. It is especially usefull for debuffs but can also be used for healing (but does not have a lot of the dedicated features of mods like Healbot). Once things are set up it can be very useful for small group to full 40 man raids.
Other mods I have found useful on some characters include:
Align : gives you a simple grid on screen to .... well make things line up !
ClassTimer : Highly configurable buff/defuf timing etc bars
CowTip : Tooltip mod that adds usefull info to the... tooltip
DoTimer : Another configurable timer - why two? Well I prefer one for some classes and the other for others - try them, play!
OmniCC : This is a cooldown counter - quite usefull as it can display info on buttons
Parrot : Scrolling combat text. Yes there is something like this built in but try it and see

RatingBuster : Breaks down an items stats to show their benefit to you eg +20 Str (40 AP)
Talented : Lets you create talent templates in game and then apply the whole template in one go.
There are a few more but these are what I would consider a core set. All should be available on curse but another place I sometimes look for things is on
www.wowinterface.com.
Lastly I often like to take a look at mods to see what a particular one adds (or subtracts from a game) but like most things in life the mileage you get from an individual mod varies with play style so there is no one size fits all !!
Above all have fun