I previously posted a detailed history of the Nebulas at one stage...as usual when I now look for it I can't find it....
Basically the Nebula Awards did not start before 1965. What they did in the early 1970s to rectify this was to publish a series of excellent anthologies selected by the SFWA for authors prior to 1965.
Whilst in more recent times the Nebulas have showcased more fantasy than before it is still traditionally thought of as an SF award.
The books and I have them and strongly recommend them, in more recent republication formats for pre 1965 stories are:
SF Hall Of Fame - Vol I 1929 - 1964 *collects the greatest short stories
SF Hall Of Fame - Vols IIA and IIB *collects the greatest novellas of all time pre 1965.
Then to confuse us even more they published two more spin-offs that I have:
SF Hall Of Fame - Vol III *1965 - 1969
SF Hall Of Fame - Vol IV *1970 - 1974
Now while that was going on the Nebula annual awards books known as Nebula Awards started up at the time of the Nebulas ONE PER YEAR which seems logical enough. I don't have these. They are:
Nebula Awards Stories 1 (1965) - Nebula Award Stories 33 (1999)
The current run of Nebula Awards is indeed called The Nebula Awards Showcase J-Sun. They began in 2000 to the current day.
I've collected them since 2006 - current and they are well worth a read.
Also while we're at it, The Hugos have not had nearly as much of a treatment as their cousins The Nebulas. Last year they released the ...wait for it... Hugo Award Showcase 2010 volume which actually collect stories from the past decade. I have that and it's quite good. Actually there are previous antecedents to this for the Hugos but that's enough of a history lesson for now I'm sure...Lol!
Also about 4 years ago I started a series of stickied threads in the Classic SF & F subforum
http://www.sffchronicles.co.uk/forum/classic-sf-and-f/ that contain a list of all key winner categories for all years that the following 'awards' have been established that at least one new member appears to have recently stumbled across....
Hugo Awards
Nebula Awards
SFWA Grandmaster Award
World Fantasy Award
Cheers.