Agfa Optima

When: 1959
Why: first fully automatic exposure, 35mm camera.

Fully automatic exposure and it's green! No batteries needed! In the next several years there were a lot of auto-exposure cameras popping up there or there, and guess what, trend continues until now. Try to find a camera without fully automatic settings. Though current cameras do require "food" out of the power lines.

Alphonse Giroux: Daguerreotype

When:1839.

Why: first "mass"-produced camera, the most valuable camera these days.

Alphonse Guroux, being a relative to Louis-Jaques-Mandé Daguerre, got an exclusive permission from Daguerre and Isidore Niépce (daughter of Daguerre's partner and inventor of the first bellows camera) to manufacture and sell these cameras. It's hard to tell how many of these cameras were manufactured exactly, but they were the first to be manufactured in quantities and to be exported to other countries. Currently these cameras are extremely rare, and prices reach close to a million of $s.

Canon: AE-1

When: 1976.
Why: First camera with the microprocessor. First SLR to be sold in millions of units.

The second "why" is actually coming from the first one. The camera was really easy to use (due to the CPU advantages), so many amateur photographers were excited to get it. More than 5 million cameras were sold in total. These days almost every film camera has a microprocessor in it. Also, microprocessor is one of the most important parts inside of all the digital cameras on the market.

Olympus: Pen F

When: 1963
Why: First 35mm half-frame SLR camera.

Compact camera with SLR features and interchangeable lenses? Here it is. This was a successful model and it was followed by Pen FT and Pen FV. Accepts a wide range of prime and zoom lenses from 20mm to 800mm.

Polaroid: SX-70

When: 1972-1977
Why: First truly folding SLR camera, First instant-film SLR camera.

Apparently Polaroid had to create an SLR camera for their instant film. Luckily they made it really portable, and it became somewhat popular. There were many variations later (I was able to find at least 28 different models). There were also non-folding models of SX-70 and numerous international versions which were similar to the USA models. SX-70 model lines were manufactured until 1986 (1982 by some sources), and the compatible film was discontinued in 2006.

Ihagee: Exakta Vest Pocket

When: 1933
Why: First 127 film SLR.
The first model was known as just "Exakta". This camera is also called Vest Pocket (VP) because of the 127 film, which was originally introduced by Kodak for its "Vest Pocket Kodak" camera. Some of the cameras were fitted with extremely fast f1.9 or f2 lens for those years, and they were called "Night Exakta".

Ihagee: Kine Exakta

When: 1936
Why: First production version of 35mm SLR, first system SLR, first interchangeable lens camera with bayonet lens mount

Ihagee was already known for the first 127 film SLR in 1933 and just in three years they introduced a first 35mm SLR too. But here is why I had to add "production" word: the first 35mm SLR prototype was a Soviet Union camera named Sport (Спорт) in 1934. Unfortunately it didn't go into production for another three years, so Ihagee stepped in first.

Hasselblad 1600F

When: 1948.
Why: First trully modular SLR camera.

Hasselblad cameras are still used by professionals (mostly) and they still have the same modular design - interchangeable everything: lens, back, viewfinder. 1600F was the first camera by Hasselblad (excluding military aicraft models) in their long line of medium format SLRs. These cameras are somewhat expensive, but they offer excellent flexibility. These days you can even get a digital back that attaches to the same film body.

Eastman Company: Kodak (Original)

When: 1888.
Why: First "point and shoot" camera for non-professional photographers.

Also, this is the first camera by George Eastman, inventor of transparent photographic film. "Point and shoot" relates to one of the best known slogans in photographic industry: "You press the button - we do the rest". And that was true. Photography enthusiasts had to press button (100 times for 100 photos on the roll) and send camera back to "The Eastman Dry Plate and Film Company" which developed film, printed photos, reloaded camera, and sent it back to customer for $10. In 1888 this pre-loaded camera was offered for $25 (kind of a high price back then), and currently it can go for up to $5000. Check out the Eastman's patent for this camera.

UPD: As it appears, George Eastman was not the "first" inventor of transparent film, nevertheless he popularized it, starting a huge change in the photography history.

Gamma Works: Duflex

When: 1947
Why: First SLR with instant return mirror.

This is the Hungarian camera, designed and built in Budapest, by Jeno Dulovits. Unfortunately focusing and viewing were separate operations but "Asahiflex IIb" came out on 7 years fixing this inconvenience. Since there were only about 800 Duflex cameras manufactured, the Asahiflex IIb one is usually called the first mass-produced SLR with instant return mirror. Currently, this feature is "a must" in any modern SLRs.

Duflex was also the first SLR to implement metal sheet focal plane shutter. Novacon site is a great source of information about this camera.