No need to do anything about the algae (it could be moss, too). It's not growing in standing water? - there are drain holes in these containers - yes?

Al

There's no standing water in the terracotta pots. Just a lot of green stuff on the inside walls. There is a large drain hole, and the pots are elevated on feet. Water drains out fast. I tried plugging the holes with foil, but a filled pot still drained out completely in a couple minutes.

I'll second that you needn't worry.
A few of my terracotta pots are developing a fine green sheen, particularly on their northern sides... ;)

Josh

Many gardeners encourage the growth on their pots, hoping to achieve a look of a very old container. Al

Mine do that all summer, and actually looks beautiful to me...Some of them got so thick with it, the pots got slimey...Especially the ones hidden behind the tall grass..My pots almost faded into the nice green grass.:-)

Mike

I don't care for that slimy feel, but the "make the pot invisible" look described by Mike sounds like an aesthetic achievement to me.

I love the look of old pots with moss on the outside, but this unfortunately does not look like that. It looks like the nasty slime that grows in a shower, but greener. Every time I look at it, I feel the urge to clean it out, but on the other hand, I have a bad back. The ugly stuff won't be seen when the pots are planted, and if it won't hurt the plants, for the sake of my poor back I should refrain from cleaning it out.

This article was in the Sunday paper, thought it was pretty interesting:

Like many objects of value, terra-cotta pots take on character as they age. The clay darkens, assuming a whitish cast from fertilizers and the minerals in water. When kept in the shade and watered frequently, the pots gradually acquire a verdant sheen of algae or moss. But you don't have to wait for that look. These six easy techniques help pots undergo a transformation within weeks. Start now and you'll enjoy their vintage charm this summer and for many seasons to come.

FERTILIZER

Accelerate the appearance of white deposits by filling the pot with a highly concentrated fertilizer solution for a few weeks. Pots aged this way are safe for plants because the salts won't wash from the pot to the soil.

Tools and materials: wine cork, candle and water-soluble fertilizer

Directions:

Plug pot's drainage hole with a wine cork. (A standard cork will fit a 10-inch pot perfectly. For smaller pots, whittle the cork; for larger ones, slice additional corks to fit, and wedge in place.)

Light candle. Let wax drip over cork on outside of pot to seal. Let cool.

Fill pot with water. (Hard water accelerates aging.)

Add five times more fertilizer than package directions recommend. The longer the pots sit, the more dramatic the effect. Remove water, wax and cork.

YOGURT

One of the most natural-looking patinas can be achieved by simply slathering plain yogurt on a new pot. Yogurt applied to dry pots yields more dramatic results. For a subtler look, first soak pots in water for 15 minutes.

Tools and materials: plain yogurt and a 2-inch foam brush

Directions:

Stir yogurt.

Use brush to coat surface of pot with yogurt, covering it completely.

Set aside in a shaded place until pot achieves the desired look, at least one month.

BUTTERMILK AND MOSS

Combining buttermilk and moss to encourage moss growth is a common tactic. The moss serves to hold the runny buttermilk in place and vary the texture, as well as to promote growth.

Tools and materials: moss (or sheet moss), buttermilk and 2-inch foam brush

Directions:

If you've gathered your own moss, remove as much soil as possible. Tear moss into small pieces, removing materials such as bark and pine needles.

Pour buttermilk into a bowl, add moss, and combine.

Use brush to paint the mixture over pot.

Set aside in a shaded place until pot achieves the desired look.

If necessary, use a metal-bristle brush to remove any heavy clumps of moss.

CLAY SOIL

It's easy to make a pot appear as if it had been unearthed in an archaeological dig. Just apply soil found in your backyard. Moist soils with high clay content are ideal, since they adhere to terra-cotta best.

Tools and materials: clay soil and flexible wire brush

Directions:

Rub soil over surface of pot, moistening the soil with a little water if it doesn't stick.

Place pot in a shaded area for at least one month while soil bonds.

Brush pot to create a varied, textured surface.

LIME

This method provides instant gratification. The lime solution quickly tones down the harsh orange of many new pots.

Tools and materials: hydrated lime (available at hardware stores), natural-bristle paintbrush, spray bottle and 150-grit sandpaper

Directions:

Dissolve 1 cup hydrated lime in 2 cups water, stirring until no clumps remain. (This amount will age several small pots or 2 large ones. You can make varying quantities of the solution, but always use 1 part lime to 2 parts water.)

Using random strokes, brush pot with lime solution, applying thickly in some areas, and thinly in others to simulate the subtle streaks of old pots.

Fill spray bottle with water, set it on the "stream" setting, and coat pot in various spots while lime is still wet. This thins the coating for a natural look. Let dry.

Sand pot in random directions, wiping dust frequently, until you have achieved the desired look.

WATER AND SUNLIGHT

Sometimes, the simplest methods bring the most satisfying results. Soak a pot in a tub of water until algae grows on its surface. Algae grows best in the sun, so be sure that vessels sit in bright locations and that water is replenished as it evaporates.

TIPS AND TRICKS

Although each technique will yield unique results, a few common truths apply to the various methods.

Ingredients: It's fine to use dairy products that aren't fresh or have expired. Low-fat products will work, but higher-fat versions tend to be thicker and therefore less likely to drip off.

Application: To achieve an authentic appearance, vary the thickness of the materials and the direction of application. Look to true aged pots for inspiration.

Storage sites: Shaded locations are ideal for most pots while they "age." Do not stack the pots. Spray them occasionally with water, or place them where rain can reach them. Pots coated with food products may smell strongly for a few days after the ingredients have been applied; keep them away from living areas.

Waiting: The longer a pot sits, the more pronounced the effect will be. It's up to you to decide when you think it's ready. Most pots will continue to "age" even as they are being used. Be creative. Try combining methods for different effects.

Here is a link that might be useful: OC Register