The Daedalus-class was an early class of Starfleet vessel that, unlike most Federation starship designs was designed with a spherical primary hull, outwardly similar to the later Olympic-class. This class, which operated with a crew of approximately 229, was decommissioned by the year 2196. (TNG: "Power Play")
Operating out of Starbase 12, the USS Essex, under the command of Captain Bryce Shumar, was lost in 2167 when the ship was destroyed with all hands aboard by an electromagnetic storm in the atmosphere of an M-class moon of Mab-Bu VI. (TNG: "Power Play")
Ships commissioned Edit
Background information Edit
Note that ship design and the name "Daedalus" have never been connected in any canon production. "Power Play" is the only mention of a ship type called "Daedalus-class". The ship model as seen on DS9, and the USS Horizon it represents, was never stated to be a Daedalus-class starship. But since the model was initially built for Star Trek Chronology to depict the Daedalus-class, we assume it is the Daedalus-class design.
While not mentioned specifically, according to dialog in "These Are the Voyages...", new warp 7 starships came into service in or sometime soon after 2161. Since the Daedalus-class is known to have been in service since at least the 2160s, this suggests that the class was among the first new warp 7 starships.
If it had been up to Designer Doug Drexler, the Deadalus-class would have been his starting point in designing the Enterprise NX-01 for the series Star Trek: Enterprise, "I like the NX-01, even though it was a frustrating experience. I’m a “canon” kind of guy. I would have liked to have seen the Daedalus style ship. You know… the sphere instead of saucer. The producers wanted it to be a saucer because they wanted it “recognizable”." wbm
Studio model Edit
According to the Star Trek Encyclopedia, this conjectural design was "based on an early USS Enterprise design by Matt Jefferies and built by Greg Jein." Jefferies himself seriously considered his design as a possible contender at the time, as he deemed the sphere the best possible pressure vessel for use in a vacuum, but eventually dispensed of as being "too bulky". (Star Trek: The Magazine Volume 1, Issue 10, p. 28) Jein built the model especially for representation in Michael Okuda's 1993 reference book, Star Trek Chronology. The model, about 20 inches long, originally bore the name USS Essex with registry number NCC-176. wbm. Interestingly, at the time the nacelles were equipped with spikes akin to those seen on the original Enterprise studio model in "The Cage".
An additional casting was taken from the molds of this model and has been refurbished as the USS Horizon, minus the spikes and with an unchanged registry, and was used as a desktop display model in Benjamin Sisko's office in Star Trek: Deep Space Nine. Okuda elaborated,
"There were at least two models of the Horizon/Essex. The first was the one that Greg built for the Chronology. I later asked Greg to make a casting of that model, so we could use it as set dressing in Sisko's office. I believe he made another casting for display at Star Trek: The Experience [remark: which he actually did, as the USS Horizon and where it was, as per plaque, specifically designated Daedalus-class ]. I may still have the original model somewhere, although I seem to recall it was damaged in an earthquake some years ago... The 'painted over stripes' were present on the cast resin copies. The original stripes were fairly thick graphic tape, so they showed up as ridges on the cast copies. Doug and I did the taping after Greg delivered the finished model. We also applied tape over the ridges on the copy in Sisko's office, at least partially, but I don't think we ever got a chance to tape the copy made for The Experience. 
"(...) Greg modeled the Daedalus for us for the Star Trek Chronology. When Doug and I were photographing it, I asked Doug to add a little bit of weathering detail to Greg's model to bring out a little more of the panel detail. We were thrilled to have a real Greg Jein model for the project, and Doug was just a bit nervous to be working on a model that had been created by one of the masters of the art. "I feel like I'm defacing a Greg Jein original," he said. I disagreed. "Look at it this way, Doug: You're actually *completing* a Greg Jein original." Faced with that unassailable logic, Doug went back to work, with beautiful results." wbm
Apart from photographing the model, Okuda also retouched the photos for representation in the Chronology/Encyclopedia by adding background and lighted windows.  While Okuda has retained ownership of the original reference model, the current whereabouts of the Sisko, and Experience display model copies are unknown, as they have not been sighted since.
In 2003 Drexler built a CGI model of the USS Daedalus with registry NCC-129 (presumably the class vessel) for use in one of James Cawley's episodes of the fan series Star Trek: New Voyages, "Almost ten years ago I had built a rough and ready CG model of this Jefferies classic for the Star Trek: New Voyages episode "In Harm's Way". The amazing Greg Jein had built a physical model of this ship for our use on Deep Space Nine, and it was seen in Captain Sisko's office through the run of the series. When it came time to bash out a CG model on my lunch break, I went down to set dressing and borrowed Greg's model from Laura. Now it sat on my desk, the best reference in the world, and I got to work. You'd love to spend a few days on something like this, but we were in the middle of making a TV show." wbm His model was later used for licensed print publications, such as the cover of the Star Trek: Vanguard novel Summon the Thunder, the Star Trek: Ships of the Line calendars and their book derivative. wbm wbm
A Daedalus-class starship named the USS Lovell is prominently featured in the Star Trek: SCE Foundations trilogy. The "Daedalus"-class starship on the book's cover is the USS Archon. The USS Lovell is also active in the Star Trek: Vanguard novels. The ship, Drexler's CGI model, is shown outside Starbase 47 (Vanguard) on the cover of the second book of the series Summon the Thunder (though Drexler had assigned the registry number NCC-129 to the USS Daedalus on his CGI model).
In Michael Jan Friedman's novel Starfleet: Year One, competition among the early Starfleet's captains for command of the first Daedalus was one of the main plot threads - though the events of this novel have been ignored by later novels, as it was contradicted by Star Trek: Enterprise.
In the Pocket ENT novels The Good That Men Do, Kobayashi Maru, and Beneath the Raptor's Wing the Daedalus-class is featured heavily as an older ship class refitted with modern technology, and the main replacement of the NX-class fleet. The NX ships were deemed too expensive and taking too long to build, shipyard personnel stated they could churn out three new Daedalus hulls in the same time it would take to build one NX vessel.