My two favorites are the Collector Particle Beam and the Arc Projector.
ZoogieZork has a good answer about why the Particle Beam is good, so I'll restrict myself to the Arc Projector.
- no travel time. Charge up, and BLAM! Lightning
- Minimal charge up time. Things like the Cain and the Blackstorm have lengthy charge up times, which can be the death of you (literally) on higher difficulties. The Arc Projector's time is fast enough that you can pop out, fire, and duck back into cover without taking any health damage.
- no self-damage. Yay for ally-friendly lightning!
- It's free DLC
- Quickly available -- selectable as soon as you get back from Freedom's Progress (If not before? Maybe? Unsure)
- Ammo Count - relatively high for a heavy weapon. Hard to waste ammo with misses (especially moving targets)
- Chain hits. The AoE potential on the Arc Projector is insane. I haven't found an upper limit on number of targets yet. If they are in a group, it is hitting everybody.
- Overloads / Stuns organic enemies, a la Reave. Will also overheat weapons a la Overload.
- not bulky or out of place on Shepard's back. (Hey, it was a big deal for me! Collector Particle Beam looks very odd if you're not wearing collector armor)
- Can duck into cover between shots.
I love it, it's a lot of fun to use. Occasionally, you'll even hit enemies you weren't expecting to. (Yay, free damage!)