To help teammates
Things like activating Weakness Policy as you've mentioned and activating abilities like Steam Engine.
Because of the secondary effects
Some moves have desirable secondary effects, but low BP. Moves with Priority, like Bullet Punch and Mach Punch, are a common example. Another example is moves that guarantee some other condition, like Nuzzle leaving the opponent with Paralysis, or Rapid Spin increasing Speed and removing Entry Hazards.
Stored Power/Power Trip
I'm guessing this counts. It's only 20 BP when you start out, and gradually gains power as you get stat increases. Shell Smash-Weak Armor-Stored Power Polteageist is a good example.
Because of abilities
Some abilities are useful with low BP moves, like Technician, or maybe Pixilate/Refigerate/Galvanize/Etc.
These are usually a bit of a gamble, unless you're using a Skill Link Pokemon. Any Multi-Hit moves have a chance to only hit 2 times, or not at all. Take Icicle Spear, for example. If it only hits twice, that's only 50 BP.