"Currently" is relative since the Black Library and the Warhammer 40K universe is ever in flux. There have been notable Imperator-Class Emperor Titans published in their works and denoted in several of the online wikis. As to whether those titans still exist in the latest productions is up to Black Library and their supplement creators.
The only still active Imperator-Class Emperor Titan I can find in records is:
Imperius Volcanus — This Emperor Class titan marched in the Novena celebrations in Hive Primaris on Thracian. Even after the terrible battle there, it was not listed as destroyed. The Two Space Marine Charters associated with it are White Scars and Aurora Chapter.
Unfortunately, Imperator-Class Titans are often at the heart of many a struggle for control of such a devastating machine. The Warhammer litanies often speak of such devices being fought over and usually destroyed to prevent them from staying in the wrong hands (the hands of whoever unearthed the device and tried to claim its holy power for their own).
A known list of Titan Legions and Traitor Legions (that is, legions who may have, can have, or potentially can get a titan from a forge world. It is not specified if they can get an Imperiator-Class, but it is indicated most large Space Marine chapters can have at least one.)
- In comparison to Battle Titans of all classes, the Imperators and Warmongers are rare with most Titan Legions only able to field three or four in a campaign. These monstrous war engines are commanded by only the most battle-hardened Princeps. Their crews are composed of the finest crew members from other Titans within the Legion. The Titan Legion's Grand Masters often use Imperator Titans as their mobile headquarters from where they can issue commands or lead vital assaults personally.
A certainly partial list of notable Imperator-Class titans:
Abominatus "Despoiler of Worlds" (Imperator-class Titan) - Abominatus is one of the most terrifying of all the servants of the Blood God. Abominatus is the hellish union of an Imperator-class Titan and a Greater Daemon of Khorne.
Aquila Ignis (Imperator-class Titan) - The Aquila Ignis was an Imperator-class Titan of the Legio Mortis, constructed in the Daedalia Forge Yards far to the south of Tharsis on Mars. The Aquila Ignis fought during the Schism of Mars against Loyalist elements from the Legio Tempestus in the battle for Magma City, where it was destroyed in the heavy combat. (Destroyed in Combat)
Dies Irae (Imperator-class Titan) - The Dies Irae was an Imperator-class Titan of the Legio Mortish which was attached to the 63rd Expeditionary Fleet under the command of the Warmaster Horus. This infamous Titan was present during the opening days of the Horus Heresy at Istvaan III, when it followed Horus' orders and helped exterminate the remaining Loyalist Astartes of the Traitor Legions present on that cursed world after they were virus-bombed by their comrades from orbit. The Dies Irae was also present during all of the major ground assaults towards the end the rebellion. The Dies Irae finally met its fate ten millennia later during the siege of Hydra Cordatus in 999.M41 during the 13th Black Crusade when it served as part of an Iron Warriors attack force. (Destroyed in Combat - Storm of Iron (Novel) by Graham McNeill)
Dominatus (Imperator-class Titan) - The Dominatus was an Imperator-class Titan from an unknown Titan Legion that fell in battle, fighting against the Forces of Chaos during the failed defence of Lorn V. Laying broken and forgotten for millennia, the lost Titan was rediscovered by the Imperium, and so, the Cadian 412th Imperial Guard Regiment, under the command of General Sturnn was despatched to retrieve it. (Destroyed in Combat - Warhammer 40,000: Dawn of War - Winter Assault and Only War: Hammer of the Emperor, Chapter 1, pg. 21)
Exemplis (Imperator-class Titan) - The Exemplis was the last remaining Imperator Titan of the Legio Ignatum, worshiped by the Adeptus Mechanicus as an avatar of the Omnissiah. The Exemplis saw its last action on the world of Tanakreg against a large Word Bearers Traitor Legion warhost of the Dark Apostle Jarulek. Despite the horrendous casualties it inflicted upon the heretics, the Chaos Space Marines managed to board and destroy the Exemplis after attacking its more vulnerable components. (Destroyed in Combat - Dark Apostle (Novel))
Mettalum Olympus (Imperator-class Titan) - The Mettalum Olympus was a notable Imperator Titan, commanded by Princeps Goethe, which managed to almost single-handedly hold off a Tyranid invasion on the ash-choked plains of Horst Prime. Surrounded by an entire horde of Hierophant Bio-Titans, the ancient Titan met its end when the Tyranids managed to breach its plasma reactor. The resultant explosion vapourised everything within a kilometre, leaving a crater that is still visible from orbit. (Destroyed in Combat - Codex: Tyranids (5th Edition), pg. 81)
Praeco Deictus (Imperator-class Titan) - An Imperator Titan of the Legio Crucius, which had survived the grim days of the Horus Heresy and had won countless victories on thousands of worlds for the Imperium. The Praeco Deictus was destroyed, along with other Titans of the Legio Crucius, defending the Hive World of Kado from the Forces of Chaos. During the fighting, a hundred Slaanesh Hell-Knights infiltrated the main Hive City and emerged to attack the Imperator Titan from the rear where it was most vulnerable, turning it into a pile of molten slag. (Destroyed in Combat - White Dwarf 190 (UK), pg. 29)