In Test cricket, Allan Border played 153 consecutive Tests, the most of any player to date (September 2015). Which bowler has played most consecutive Test Matches?
Sure, from the list of most consecutive test match appearances (link), filtering out the specialist batsmen and all-rounders, we get:
Anil Kumble, who played in India's 60 consecutive tests between 18 Oct 1992 and 2 Mar 2000. He is at 33rd position on the list.
If we include all rounders under bowlers, the "winner" is:
Sir Gary Sobers, who played in West Indies' 85 consecutive tests between 11 Apr 1955 and 20 Apr 1972.
Depends on how you define a bowler - Border has 39 test wickets, so he could qualify!
Based on the Cricinfo appearances list, the first player not primarily identified as a batsman (that I can see) is Garfield Sobers, who was an all-rounder. The first primary bowler I can see is Anil Kumble (not Glenn McGrath as previously stated).
Note that this is from a quick scan of the list, and opinions may vary.