I'm writing some fiction, and a male character was born in Sweden in
the late 1980s. I would like to have a good long list of given names
to look at that would be common from that time period. (In other
words, I wouldn't want to give him a name that sounds "older" to a
Swedish person, much like the American names Earl, Betty, Martha, or
Gladys.)

The Swedish website Svenska Namn ("Swedish Names",
http://www.svenskanamn.se) has lists of the 100 most popular male and
female names for each year back to 1989.  The 1989 list for boys'
names is (numbers indicate how many got the name in 1989):

Johan (1905)
Robin (1629)
Fredrik (1615)
Kristoffer (1612)
Markus (1588)
Andreas (1565)
Daniel (1531)
Niklas (1372)
Erik (1348)
Simon (1264)
Mattias (1258)
Alexander (1193)
Viktor (1190)
Joakim (1148)
Martin (1095)
Mikael (1079)
Tobias (995)
Emil (974)
Jonas (966)
Sebastian (880)
Oskar (865)
David (823)
Patrik (769)
Anton (764)
Karl (758)
Henrik (675)
Kristian (668)
Jimmy (632)
Jonatan (625)
Rikard (623)
Filip (615)
Linus (610)
Jesper (568)
Robert (528)
Adam (520)
Gustav (497)
Jakob (493)
Dennis (470)
Kim (440)
Anders (433)
Pontus (418)
Magnus (395)
Joel (393)
Rasmus (392)
Per (373)
Peter (348)
Tomas (348)
Jens (331)
Björn (323)
Stefan (313)
Hampus (296)
Tim (294)
Johannes (293)
John (290)
Tommy (279)
Max (260)
André (226)
Axel (205)
Olof (189)
Johnny (179)
Ludvig (171)
Tom (170)
Petter (162)
Lars (159)
Pierre (146)
Jim (139)
Nils (134)
Samuel (131)
Albin (127)
William (117)
Isak (113)
Olle (112)
Lukas (111)
Elias (109)
Dan (107)
Timmy (96)
Hannes (95)
Felix (92)
Oliver (89)
Gabriel (88)
Josef (88)
Tony (88)
Kalle (87)
Kenny (86)
Klas (83)
Benjamin (82)
Ola (81)
Arvid (78)
Ted (75)
Jerry (73)
Emanuel (72)
Mats (68)
Mårten (65)
Krister (64)
Håkan (62)
Jon (61)
Kevin (61)
Charlie (61)
Morgan (61)
Eddie (57)

(Source: http://www.svenskanamn.se/top_hundred.asp?year=1989)

Another Swedish webpage, Svenska Förnamn ("Swedish Given Names",
http://hem.passagen.se/louise.kj/)  has lists of Swedish names typical
for each decade in the 1900s; however, this page does not cite any
sources or give any frequencies for the listed names.  The list of
boy's names from the 1980s are:

Johan  	   	
Jonas 	  	
Daniel 	  	
Martin 	  	
Andreas 	  	
Tobias
Mattias
Jens  	
Robin  	
Jimmy

(Source: http://hem.passagen.se/louise.kj/poattio.htm)

With the exception of "Jens", all these names are among the top 30
names of 1989 (Jens is listed 48th).

I believe this information answers your question.  If not, please
request an asnwer clarification before you rate this answer.

Search term used on google.com: "pojknamn 1980 OR 80-talet"

Fantastic. That's exactly what I wanted. Thank you!