JaccoW

Koga-Miyata was founded in 1974 by Andries Gaastra, son of the founder of Batavus. While studying in Germany he met his wife and he came back to work for his father at Batavus in 1967.
When his father sold the brand in 1974 he told his wife he didn't want to stay and begin a brand for himself. Together they started Koga trading by the end of 1974. The name is a substraction of his wife's surname Marion Kowallik and Gaastra.
Koga thought there was room for a really upscale bicycle manufacturer in the Netherlands (Holland) using high-quality Japanese parts. They contacted Miyata because they though the company would be able to supply them with high-quality frames at a good price.
The name Koga-Miyata came forth from this partnership and design and assembly were done in the Netherlands.

The company started building racing models (Pro-Racer, Pro-Luxe & Road-Racer) in 1974, added a touring model (GentsTouring) in 1976 and a Dutch commuter bike (SilverAce AL & SilverAce ST, 3-speed Sturmey Archer) in 1982. Apparently the were one of the first to sell mountain bikes on the Dutch market in 1983-1984 (RidgeRunner & TerraRunner-E) though you won't see them in brochures until 1986. Late 80's Koga-Miyata was a respectable player on the Dutch market, and tested their frames in California, but that faded by the time the 90's came around. Most likely because there were cheaper imports coming in from the US by that time and Koga-Miyata's were relatively heavy, though indestructible, in the pre-suspension days. For the other frames the increasing price of the Yen was also a big issue as the frames were imported from Japan.

1989 saw the introduction of several alloy frames (SkyRunner & SuperWinner Alloy) and lugged carbon fibre frames with an alloy inner tube Carbolite®-7 & Carbolite®-3 (FullPro-Carbolite & Pro-Carbolite). Still all of them made my Miyata.
Around 1995 they moved production to Taiwan under Miyata's supervision and according to Koga⁶ they haven't used any steel frames from Miyata since 1998.
As far as I can tell they continued to use Miyata frames until 2005 (FullPro-C) but after that it was all 7005 Alloy and Carbon fibre.

Some call the 1999 year when they celebrated their 25th anniversary a dark year. By 1997 they had phased out most of the steel frames for aluminum models and they were sometimes innovating just for the sake of change and making weird component choices. Examples of this are the unfortunately chosen Sachs Elan 12-speed hub in the 1999 LiteAce model, which had a history of breaking and at 3.4kg (7.5lbs) was a boat anchor, or some of the early 2000's alloy suspension frames, which had a tendency to break the frame.

Nowadays they are making excellent high-quality bikes again. Even our current Prime Minister Mark Rutte rides a Koga.

In 2010 they announced they would stop using the Miyata part of their name and would contiunue in 2011 as Koga.
2013 they became part of the Accell group, the biggest bicycle manufacturer in Europe.

They have always been seen as a high-end brand over here in the Netherlands and they seem to hold their value well (Marktplaats) on the second hand Dutch bicycle market. The bikes come in understated colours, are often fully loaded and well finished. Even their racing bikes usually came with branded pumps though the designs are not as unique as they used to be.
Koga-Miyata always had a few more practical parts and details compared to their Miyata counterparts like a holder for CO² cartridges (1989 ProDelta), a shifter to engage the bracketdynamo on the seattube (1989 Randonneur-Extra) or stainless steel handlebars and screws (1982 SilverAce ST) or the modern Koga Denham touring handlebars that offer both a wide grip as well as the aero position of a drop handlebar.

IMHO Koga(-Miyata) buyers are generally more affluent or older people that are willing to spend for high-quality pre-made bikes. They are generally well-thought out and offer plenty of innovation without going full proprietary like Gazelle has a tendency to do.
Which nowadays makes for some well-maintained second-hand bikes.

Sources:

1. Interview with Andries Gaastra 2009 - by Eric Schuijt - Owner of the Vakantiefietser Amsterdam
2. User Elevation12,000 over at forums.mtbr.com
3. The legendary Koga-Miyata - Lovetoridemybicycle
4. Koga-Miyata - Classic Rendezvous
5. Miyata VS Koga Miyata - BikeForums
6. Corporate Spotlight: KOGA Bicycles - AdventureCycling
7. Koga-Miyata Kimera - Mediamatic
8. Koga-Miyata - Retrobike
9. VintageMiyata
10. Some additions by me