Atmospheric entry, or reentry, was when a spacecraft made an entry into a planet or moon's atmosphere from space. At high speeds this could compress the air in front of the craft, producing high temperatures that could be lethal to an inadequately-shielded vessel.
In 2152, the criminal Kuroda Lor-ehn placed his stolen Enolian prison transport into a decaying orbit over Tamaal, planning to let the craft disintegrate in the atmosphere while he, his Nausicaan accomplice, Jonathan Archer, and Charles Tucker III escaped on an Enolian shuttle. Ultimately, Kuroda went down with the ship while Enterprise NX-01 rescued everyone else. (ENT: "Canamar")
In 2259 of the alternate reality, the USS Enterprise fell into Earth's atmosphere after being disabled by the USS Vengeance over Luna. The vessel suffered damage during re-entry but was saved from crashing into the surface after Captain James T. Kirk managed to restore main power. (Star Trek Into Darkness)
In 2267, Montgomery Scott suggested to Spock that if they timed their flight aboard the Galileo, they could cut their orbit and save enough of their fuel for a controlled re-entry into the atmosphere of Taurus II. Spock instead elected to dump and ignite the fuel, signalling the nearby USS Enterprise to beam the Galileo crew aboard before the shuttle re-entered and burned up. (TOS: "The Galileo Seven")
In 2364, the shuttle Copernicus nearly fell into the atmosphere of Relva VII after its pilot, Jake Kurland, accidentally depowered its dilithium core. Captain Picard was able to coax him into piloting it into a shallow reentry trajectory; in this trajectory, the Copernicus rebounded off the planet's atmosphere and was safely recovered by the USS Enterprise-D. (TNG: "Coming of Age")
Later that same year, the Enterprise-D defeated a cloaked Echo Papa 607 by entering the atmosphere of Minos; when the drone pursued, it became visible due to the surrounding plasma and was easily destroyed. (TNG: "The Arsenal of Freedom")
Also in 2364, the Ornaran freighter Sanction became trapped in a decaying orbit over Ornara after losing power. The Enterprise-D rescued four of the six passengers, as well as their cargo of felicium, before the Sanction was destroyed in the atmosphere. (TNG: "Symbiosis")
In 2371, the Enterprise-D's saucer section fell into the atmosphere of Veridian III after losing helm control. The damaged vessel crash-landed on the planet after surviving re-entry. (Star Trek Generations)