Reducing the amount of hate you pull is a lot easier as you level higher.
Keep in mind...
AoE Heals (Medica) is a HUGE hate grabber. Don't use it UNLESS you absolutely have to (lots of people are taking consistent damage or you don't have time to heal people up individually).
Regen is a great way to heal someone without pulling a lot of hate. Use it on a DPS who took just one hit. Keep it rolling on the tank, but NEVER throw it on a tank before they make a pull (if it's a multi-pull and the tank doesn't grab hate right away, you could be pulling the adds).
Stoneskin is a good way to negate damage, but it isn't always mana-efficient. I like to throw it up on the tank when he's full to prevent more unnecessary heals. Throw it up on DPS when there is a lull in activity (before pulls, for example).
Wait until your cures are most 'mana-efficient' before you cast them. It's generally better to keep casting Cure I until you get a proc (Freecure) for Cure II UNLESS the tank is taking too much damage to keep up with Cure I. With that said, don't be shy about using heavier cures when it's needed.
Shroud of Saints is both a mana regen and an aggro drop. Use it wisely once you get it! Watch the aggro on the enemy bars (if you are approaching orange, you should probably use it).
If you are following the advice of everyone in this thread and are still pulling hate... the problem may be someone else. People like to point fingers when they ideally should be helping others learn. =/