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This list includes 30 players who averaged more than 13 rebounds per game in any season, but did not play in any NBA All-Star Game.
Nate Thurmond tops the list with almost 20 rebounds per game in 1968-1969. In second place appears Bill Russell, who missed the NBA All-Star Game in his rookie season because he started to play late in December because he was playing in the Olympics (Melbourne 1956).
There are a lot of players with multiple appearances on this list, but Dennis Rodman with 6 seasons (all of them in the Top 16) clearly stands out. Four players are shown 3 times on the list: Walt Bellamy, Bill Bridges, DeAndre Jordan, Nate Thurmond and Wes Unseld. There are another eight players with 2 presences.
Stats updated until 2015-2016 regular season.

Rk Player Season Age TRB G ORB DRB TRB
1Nate Thurmond1968-692719.7711402
2Bill Russell1956-572219.648943
3Dennis Rodman1992-933118.3623677651132
4Dennis Rodman1993-943217.3794539141367
5Dennis Rodman1994-953316.849274549823
6Wes Unseld1969-702316.7821370
7Dennis Rodman1996-973516.155320563883
8Nate Thurmond1971-723016.1781252
9Walt Bellamy1965-662615.7801254
10Elmore Smith1971-722215.2781184
11Bill Bridges1970-713115.0821233
12Dave Cowens1970-712215.0811216
13DeAndre Jordan2014-152615.0823978291226
14Swen Nater1979-803015.0813528641216
15Dennis Rodman1997-983615.0804217801201
16Dennis Rodman1995-963414.964356596952
17Red Kerr1961-622914.7801176
18Clyde Lee1971-722714.5781132
19Bill Bridges1968-692914.2801132
20Tom Boerwinkle1970-712513.8821133
21DeAndre Jordan2015-162713.8772677921059
22Clyde Lee1968-692413.865897
23Nate Thurmond1970-712913.8821128
24Ray Scott1967-682913.7811111
25Kenny Sears1959-602613.764876
26Gus Johnson1963-642513.6781064
27DeAndre Jordan2013-142513.6823317831114
28Walt Bellamy1966-672713.5791064
29Bill Bridges1971-723213.5781051
30Andre Drummond2014-152113.5824376671104
31Happy Hairston1973-743113.5773357051040
32Ray Scott1963-642513.5801078
33Red Kerr1957-582513.472963
34Sam Lacey1973-742513.4792937621055
35Walter Dukes1958-592813.372958
36Walter Dukes1957-582713.372954
37Mel Hutchins1951-522313.366880
38Wes Unseld1979-803313.3823347601094
39Wes Unseld1975-762913.3782717651036
40Andre Drummond2013-142013.2814406311071
41Swen Nater1977-782813.2782787511029
42Ben Wallace2000-012613.2803037491052
43Marcus Camby2007-083313.1792308071037
44Happy Hairston1971-722913.1801045
45Bill Laimbeer1985-862813.1823057701075
46Jerry Lucas1971-723113.1771011
47Moses Malone1976-772113.1824376351072
48Charles Oakley1986-872313.1822997751074
49Walt Bellamy1972-733313.074964
50Michael Cage1987-882613.072371567938
51Artis Gilmore1976-772713.0823137571070
52Dikembe Mutombo1992-932613.0823447261070
53Charles Oakley1987-882413.0823267401066
Provided by View Original Table
Generated 2/1/2017.

And this is the same list, but only displaying players with 12+ rebounds per game in any season that never have been selected for the NBA All-Star Game.
14 players with some of them making multiple appearances: Swen Nater 4 times, Happy Hairston 3 times, and Tom Boerwinkle, Ray Scott and Elmore Smith with 2.
There are no active players on this list.
Stats updated until 2015-2016 regular season.

Player Season Age TRB G ORB DRB TRB
Elmore Smith1971-722215.2781184
Swen Nater1979-803015.0813528641216
Tom Boerwinkle1970-712513.8821133
Ray Scott1967-682913.7811111
Happy Hairston1973-743113.5773357051040
Ray Scott1963-642513.5801078
Swen Nater1977-782813.2782787511029
Marcus Camby2007-083313.1792308071037
Happy Hairston1971-722913.1801045
Michael Cage1987-882613.072371567938
Happy Hairston1974-753212.874304642946
Rich Kelley1978-792512.8803037231026
Marvin Webster1977-782512.6823616741035
Tom Boerwinkle1969-702412.5811016
Swen Nater1980-813112.4822957221017
Elmore Smith1972-732312.476946
Neal Walk1972-732412.4811006
Leroy Ellis1970-713012.374907
Clifford Ray1973-742512.280285692977
Larry Smith1980-812312.182433561994
Pete Cross1970-712212.079949
Swen Nater1976-772712.072266599865
Provided by View Original Table
Generated 2/1/2017.