As a Distraction
The most obvious use for the critters for distracting enemy defenses. Critters cost initially 8 gunboat energy, and increase by 5 per use. This means that 3 salvos of critters costs 39 Gunboat Energy (Abbreviated GBE) and yield 18 critters for a level one critter shot.
As you can see, all of the defenses in range are targeting the critters which are closer to them rather than my troops.
It is likely that Supercell added critters to the game with this in mind, as critters can set off one or two mines each depending on the level of the mines and the critters. Drop a few salvos on mines or boom mines to protect troops like riflemen and zookas!
For Distant Buildings
Critters have a small but noticeable offensive capability.
With the addition of critters in Boom Beach, hiding buildings in the back of your base is now a very foolish strategy. One or two salvos of critters can take out these buildings and earn you GBE as well as damage towards the HQ.
As Low-Cost Damage Sponges
Critters can be useful for absorbing hits from high damage dealing defensive structures such as boom cannons. Rather than let your troops get demolished by a few shots from a cannon or boom cannon; buy your troops some time and reduce casualties by dropping critters on these pesky defensive buildings to absorb an entire Boom Cannon shell instead!