The New General Catalog was published in 1888, by the Danish astronomer JLE Dreyer. Extended by two Index Catalogs (IC), the catalog lists 13,000 objects in total.
Some of the more well-known are listed here
NGC 104, 47 Tucanae
NGC 869/ NGC 884, Double Cluster in Perseus (h and chi Persei)
Found in the region between Perseus and Cassiopeia, separated by about 0.6 of a degree. They are actually close together in the Galaxy, in the Perseus arm, at a distance of 7000-8000 light years.
NGC 1555, Hind's variable nebulae
Surrounds the variable star T Tauri. It is one of three nebulae known to change shape on fairly short timescales, by virtue of the light from the relevant star varying. Has not been seen visually for over 70 years but can be recorded photographically or with CCDs.
NGC 2070, Tarantula Nebula, 30 Doradus Nebula
In the Dorado constellation. It is actually in the Large Magellanic Cloud. It is the largest of the numerous pink nebulae in the LMC (of which there is an image below).
NGC 2237, Rosette Nebula
In Monoceros. Also contains an galactic cluster NGC 2244.
NGC 2264, Christmas Tree Nebula
NGC 2392, Clownface Nebula, Eskimo Nebula
In Gemini and discovered by William Herschel in 1787. Considered to be a challenge for amateurs.
NGC 3372, η Carina NebulaIt surrounds the star η Carinae which was noticed to be a variable by Edmond Halley in 1677. In 1843, it was competing with Sirius to be the brightest star in the sky, but nowadays has been below sixth magnitude. Another (dark) nebula, NGC 3324, the Keyhole Nebula, is superimposed on NGC 3372.
NGC 4755, The Jewel Box
In Crux. Small but has stars of several colors.
NGC 5128 (Centaurus A)
Visually, distinguished by a dark band that crosses its center, As a strong radio source, it is known as Centaurus A, emiting more than 1000 times as much radio energy as the Milky Way.
NGC 5139, ω Centauri
It is of fourth magnitude, so bright it was given a stellar designation, ω-Centauri, by Johann Bayer. It is the brightest Globular Cluster in the sky.
NGC 6960, 6992, 6995. Vela Nebula
Supernova RemnantFurther details here.
NGC 7000, North American Nebula
Lies 3° away from Deneb. It is hard to find because of its size (1.5°) and its faintness per unit area. Its magnitude is four but this is obviously accrued from a large area -it can therefore be easier to see with the naked eye than thru a telescope. It gets its name from its shape in photographs, a shape which is not apparent when viewing with the eye.
NGC 7293, Helix Nebula>
The nearest and brightest Planetary Nebula is NGC 7293 in Aquarius, which was not included in Messier's list. In the South of the constellation of Aquarius.
IC 434, Horsehead Nebula
Commonly seen in photographs but hard to see visually. Close to Orion's belt, just below the leftmost of the three stars in the belt.