Answer seems to be in what you count as a way. 23 seems to be the highest claim. I'm not sure what I count as a legit unique way.
According to Eric Enders, a researcher with the Baseball Hall of Fame, there are 23 legal ways to get to first (but 2 fewer ways for a batter to do so); my comments are in brackets: 1. walk 2. intentional walk [this is now scored separately from a walk, and records are kept; Barry Bonds just broke his old season record a few weeks ago] 3. hit by pitch 4. dropped third strike 5. failure to deliver pitch within 20 seconds [yes, it might be scored as a ball, but it doesn't involve throwing the ball outside the strike zone and violates a different rule] 6. catcher interference 7. fielder interference 8. spectator interference ("the act of a spectator touching a live ball by reaching out of the stands or going on the playing field") 9. fan obstruction [truth be told, I have no idea how this differs from spectator interference] 10. fair ball hits umpire 11. fair ball hits runner 12. fielder obstructs runner 13. pinch-runner [does not apply to batter] 14. fielder's choice [which may not result in an out anywhere] 15. force out at another base 16. preceding runner put-out allows batter to reach first 17. sac bunt fails to advance runner [I would have thought this was just a fielder's choice] 18. sac fly dropped [I would have thought this was just an error] 19. runner called out on appeal 20. error 21. four illegal pitches [yes, scored as balls, but again, not necessarily involving 4 pitches outside the strike zone] 22. if a game is suspended with a runner on first and that player is traded prior to the makeup, another player can take his place [does not apply to batter, and I imagine this would apply if the original runner was not available for other reasons, such as illness, injury, etc.] 23. hit Some of these may be scored similarly, but they are all apparently distinct ways to get to first.
According to Eric Enders, a researcher with the Baseball Hall of Fame, there are 23 legal ways to get to first (but 2 fewer ways for a batter to do so); my comments are in brackets: 1. walk 2. intentional walk [this is now scored separately from a walk, and records are kept; Barry Bonds just broke his old season record a few weeks ago] 3. hit by pitch 4. dropped third strike 5. failure to deliver pitch within 20 seconds [yes, it might be scored as a ball, but it doesn't involve throwing the ball outside the strike zone and violates a different rule] 6. catcher interference 7. fielder interference 8. spectator interference ("the act of a spectator touching a live ball by reaching out of the stands or going on the playing field") 9. fan obstruction [truth be told, I have no idea how this differs from spectator interference] 10. fair ball hits umpire 11. fair ball hits runner 12. fielder obstructs runner 13. pinch-runner [does not apply to batter] 14. fielder's choice [which may not result in an out anywhere] 15. force out at another base 16. preceding runner put-out allows batter to reach first 17. sac bunt fails to advance runner [I would have thought this was just a fielder's choice] 18. sac fly dropped [I would have thought this was just an error] 19. runner called out on appeal 20. error 21. four illegal pitches [yes, scored as balls, but again, not necessarily involving 4 pitches outside the strike zone] 22. if a game is suspended with a runner on first and that player is traded prior to the makeup, another player can take his place [does not apply to batter, and I imagine this would apply if the original runner was not available for other reasons, such as illness, injury, etc.] 23. hit Some of these may be scored similarly, but they are all apparently distinct ways to get to first.