MIT aeronautics professor and engineer Dava Newman has been trying for a number of years to talk NASA into a better space suit. Now that a number of possibilities are opening up in terms of non-NASA space travel, maybe we'll see some progress.
Dava’s suit would be a huge leap forward in terms of construction as well. They’ve enlisted the expertise of Dainese, an Italian manufacturer of motorcycle racing “leathers”—leather and carbon-fiber suits designed to protect racers traveling at up to 200 mph.
The suit would be a degree safer than current space suits. While a puncture or scrape in a traditional space suit would cause a dramatic decrease in pressure and would be tramatic, even deadly The “biosuit” could be patched with a high tech ace bandage. The wearer would wrap it around the punctured area to stop the leak almost instantly. Pressure loss would be minimal and the astronaut would be able to continue working and finish his or her task.
The earliest reference I know about for a space suit is the "air-tight suit" from Garrett P. Serviss' 1898 story Edison's Conquest of Mars:
While it was the intention to remain as much as possible within the cars, yet since it was probable that necessity would arise for occasionally quitting the interior of the electrical ships, Mr. Edison had provided for this emergency by inventing an air-tight dress constructed somewhat after the manner of a diver's suit, but of much lighter material. Each ship was provided with several of these suits, by wearing which one could venture outside the car even when it was beyond the atmosphere of the earth...
(Read more about Serviss' air-tight suit)
As far as I know, the first use of the word "space-suit" was in The Emperor of the Stars, published in 1931 (see space-suit).