If you're starting seeds indoors, it's common to find that, all of a sudden, there is green algae growing on the surface of your seed starting mix. This is very common when using peat-based mixes, which is what most gardeners tend to use for seed starting. The good news is that it's not likely to harm your seedlings, and it's fairly simple to prevent.
To clear up any green algae growing on your seed starting mix, just lightly cultivate the surface of the soil with a small tool, such as a chopstick or pencil, to break up the layer of algae.
The algae itself won't hurt your seedlings, but if you allow it to keep growing, it could eventually get thick enough that it could start to hold too much moisture near the seedling's stem, which can lead to rot (according to Dr. R.E. Roberts, Texas A & M).
What causes the algae is soil that stays too moist, for too long, as well as a lack of air circulation. If you've been watering from the top, try watering from the bottom instead, by filling the tray your seedlings are in with about an inch of water. Whatever water isn't absorbed after an hour should be poured out so you don't rot your seedlings.
Also, to help with air circulation, I like to keep an oscillating fan on low near my seed starting racks. This will keep your plants from staying too damp, and will also encourage stronger growth.
By following these steps, you can avoid the algae in the first place. But, remember, it's not really such a big deal if it shows up.
Just ease up on the watering and provide better ventilation: problem solved.