if you are storing rainwater for human consumption, you need to treat it before drinking. there are just too many different, and wirse things, than algae to worry about in STORED rainwater.

our bodies are so used to all the treatments in things now that they no longer fight off bacteria like in the old days. back 100 years ago folks collected rainwater and stored it for a long time, and they rarely got sick since their bodies were used to the types of bacteria in it. no different than if you or I went to Mexico the water could make us sick to our stomachs, yet Mexicans drink it every day to no ill effect.

As has been stated before, do not drink collected and un-treated rainwater.

For watering plants etc, if your rain water grows algae, thats not a bad thing. Algae are great for soil amendment.

If you don't want the algae, buy a couple "algea eaters" from the local pet/aquarium store.