What are the easiest corals to grow?

Short answer

Soft corals are the easiest: green star polyps, zoanthids, mushrooms (Discosoma, Rhodactis), Xenia (pulse and non-pulse), Sinularia and Sarcophyton leathers, Kenya Tree. They tolerate parameter swings, low light, and beginner-level dosing. Avoid SPS (Acropora, Montipora), anemones, and Goniopora until your tank is mature.

In depth

Easy coral does not mean less impressive coral. Some of the most attractive reef tanks are 80% soft coral and zoanthids. The "easy" tag means parameters can drift slightly, lighting can be moderate, and the coral forgives the kind of mistakes new reefers inevitably make.

The easy-coral list

Green Star Polyps (GSP) - aggressive grower, tolerates almost everything, but will overgrow rock if not managed. Plant on an isolated rock.
Zoanthids and Palythoas - hundreds of named cultivars, very forgiving, color up under most LED spectrums. Wear gloves when handling - palytoxin is real.
Mushroom corals (Discosoma, Rhodactis) - low-light, low-flow, will multiply on their own. Bounce mushrooms (premium Rhodactis) are the showpieces of this group.
Xenia (pulse and non-pulse) - the pulsing motion is mesmerizing. Tolerates lower nutrient levels than most coral.
Toadstool leather (Sarcophyton) - grows slowly into a centerpiece coral. Periodic shedding of waxy slough is normal.
Kenya Tree (Capnella) - branches readily, easy to frag, tolerates low flow.
Pulsing Xenia - one of the few corals that visibly moves on its own, needs zero feeding.

Then graduate to easy LPS

Once you have 6+ months of stable parameters, hardy LPS opens up: Trachyphyllia (open brain), Caulastrea (candy cane), hardy Euphyllia like hammer and frogspawn (skip torch coral until later), Acanthastrea, Lobophyllia.

The hard list, save for later

SPS (Acropora, Montipora), Goniopora, anemones, and most chalices need a tank that has been running stable for at least a year. Buying these as a beginner is the fastest way to lose $400 in 30 days.