The Turbinaria peltata or Cup Coral is a relatively easy coral to keep. It does best under moderate lighting, and can be feed plankton-sized foods if necessary. It will grow in mass, getting wider over time. Watch the leading edges where new polyps form, displaying that new growth. It comes in a couple of colors, such as golden brown or green, as pictured.
Turbinaria sp. - Turbinaria reniformis more than likely - isn't the first coral you think of when adding livestock to your aquarium, but once you see some in another tank you realize you've been missing out far too long! The Yellow Scroll coral will grow in layers, forming cups and ripples as it matures in your reef.
Read the story about this coral here: http://www.reefaddicts.com/entry.php/29055-Yellow-Scroll-coral-over-time
The favia coral nicknamed War Coral is a popular choice. Its name is derived from the way the colors are segmented by barriers, more than likely.
Here is a coral many people fall in love with, but it needs some TLC to keep it alive and happy. These grow in ocean caves, typically upside down. I got this Sun Coral - Tubastrea - in a trade with a club member, feeding it nearly daily with mysis shrimp. Because my clownfish seem to think my hand is dangerous and nip at me, I've created a feeder with a turkey baster and a length of flexible tubing to drizzle the thawed food over each polyp. Feedings take about 15 minutes, and I turn off the pumps while doing so.
Goniopora is a difficult coral to care for, usually best for more experienced reef keepers. Basically, it needs a nutrient laden environment to thrive, and our tanks are often too pristine. The Red Goniopora is considered the hardier one, compared to the abundance of green ones for sale. They die slowly over time, receding from the skeletal base. Success can only be measured in years of captivity, and few are able to do so. I purchased this one from a reefer that kept it for nine months.
This LPS is about 6" long and 4.5" wide and 3" tall. It is a brain coral, called Platygyra pini. It is another coral that filter feeds at night, extending small polyps from the openings to capture planktonic-sized foods.
This is a coral from the Bubble family. It has been suggested it might be a Pearl Bubble Coral, but I've not seen one like this before. As you may have considered, it kind of looks like a Ricordea. This one has a mixture of pink and green bubbles. At night, it looks far different. Bubble corals are LPS corals, and need gentle to medium flow, and reef parameters to thrive.
Similar to Frogspawn, this LPS coral is nicknamed Octopus Coral or Octospawn. Its needs are the same as any LPS, which includes good lighting, moderate flow, and stable water parameters. It doesn't need to be target fed, but will eat diced meaty foods at night. The nickname is likely due to the abundance of dots, similar to all the sucker cups of an octopus. Octospawn are often lighter or more pale that their Frogspawn counterpart.
Neon green Candy Cane corals add some eye candy to a reef tank. This is an LPS (large polyped stony) coral, which when cared for properly will continue to grow and split, making new heads. Essentially a night feeding coral, short tentacles extend to trap any food in the water column. Under actinic lighting, these corals glow brightly. Good water quality is a must. LPS corals need calcium so they can continually build the base structure. Fragging this coral is possible by carefully breaking the branches at the base.
This is sometimes referred to as a "moon coral", but it is a Favia sp. This specific specimen is multicolored, and at night when it feeds, it looks positively furry and 100% different in appearance. It isn't a hard coral to keep, but keep other corals away from it to avoid chemical stings that may hurt it.