Most orchids are making vegetative growth to prepare them for fall or spring flowering seasons, but a few put on a summer show.
Some Catasetum and Cycnoches hybrids spiking. Their large leaves require a LOT of water, so do not let these plants dry out until their pseudobulbs are fully ripe in the fall and dormancy begins. Look for spikes on Ctsm barbatum, Ctsm Karen Armstrong, Ctsm pileatum and many of its hybrids.
Late-spring Cattleyas are still flowering, including C. tenebrosa, C. lobata. Bifolate cattleya hybrids bred from C. aurantiaca, C. bicolor, C. loddigesii, C. harrisonianum, C. intermedia and C. guttata are budding. June blooming hybrids also include C. Aurantimedia, SC Beaufort, SLC Hazel Boyd, SLC Tangerine Imp, SLC Madge Fordyce.
Encyclia, Epidendrum and Prosthechea species and hybrids love summer! Epidendrum difforme, Epi. pseudoepidendrum; Encyclia alata, E. atropurpureum, E. cochleata, E. radiata, E. tampense and their hybrids (such as Epicattleya Rene Marques) will be blooming.
Phalaenopsis amboinensis, P. bellina, P. cornu-cervii, P. mannii, P. luddemanniana, P. violacea, Doritis pulcherrima, and many other waxy-flowered Phals (especially hybrids) enjoy this season, after their big showy relatives die back and start growth season. They will continue to make new buds and flowers, a few at a time, all summer and fall. Mature plants will produce stronger, longer-lasting spikes that can flower for over a year. Miniature Phalaenopsis hybrids will still produce branches on their main spikes, if you do not cut them.
Season-indeterminate hybrids -- from Brassavola nodosa, or Oncidium Alliance hybrids for example -- will bloom any time of year, on any mature growths. Also some "year-round" modern Masdevallia hybrids like M. Copper Angel will grow and flower even in the summer, if they are kept cool and comfortable.
Terrestrials Habenaria medusa and H. rodochila should be waking from their long winter/spring dormancy. Remember to never let the potting mix go completely dry for too long if you keep the plants indoors, as the tubers will over-dry and die. (All that advice online about not watering a dormant plant is meant for GREENHOUSE people with very high humidity.)
Stanhopeas make summer spikes now that it’s warm and sunny. While the flowers may only last a few days, a healthy mature plant will make multiple spikes so that you always have buds and flowers
Many Vanda Alliance plants love summer too, everything from big hearty hybrids like V. Fuchs Delight to midsize Ascda Princess Mikasa and Aerides odorata, to small Ascofinetia Cherry Blossom will bloom their best given plenty of light, warmth and humidity. (Some hybrids will bloom spring, summer and fall.)