The St. Louis Browns have stolen the most bases by a team in a season, with 581 steals in 1887.

which team has the most stolen bases in a season
1887Browns1887Orioles1887Red Stockings1887Athletics1889Cowboys1888Red Stockings1888Browns1887Colonels1889Red Stockings1891Reds1896Orioles1888Athletics1890Maumees1887Giants1890Reds1892Grooms1887Grays1897Orioles1889Bridegrooms1887White Stockings1887Beaneaters1899Orioles581545527476472469468466462447441434421415412409409401389382373364
TEAMSEASONGSBW%WLABRH2B3BHRRBISHSFCSBBIBBHBPSOGIDPPATBXBHAVGOBPSLGOPS
St. Louis Browns1887138581.70495405,0481,1311,5502617839862442673425,5572,084378.307.371.413.783
Baltimore OriolesBaltimore Orioles1887141545.57077584,8259751,33720210031765469683375,3621,832333.277.349.380.729
Cincinnati Red StockingsCincinnati Red Stockings1887136527.60081544,7978921,28517910237678382563795,2351,779318.268.329.371.700
Philadelphia AthleticsPhiladelphia Athletics1887137476.48164694,9548931,3702318429661321513795,3261,856344.277.327.375.702
Kansas City Cowboys1889139472.40155824,9478521,2561627618621430666265,4431,624256.254.322.328.650
Cincinnati Red StockingsCincinnati Red Stockings1888137469.59780544,8017451,1611328232571345605595,2061,553246.242.301.323.624
St. Louis Browns1888137468.68192434,7557891,1891494736591410505205,2151,540232.250.316.324.640
Louisville Colonels1887139466.55976604,9169561,4201949827728436403675,3921,891319.289.352.385.736
Cincinnati Red StockingsCincinnati Red Stockings1889141462.54776634,8448971,3071979652696452605115,3561,852345.270.340.382.722
Boston Reds1891139447.68993424,8891,0281,34116310052776651664995,6061,860315.274.367.380.748
Baltimore OriolesBaltimore Orioles1896132441.69890394,7199951,54820710023854983861202015,3232,024330.328.393.429.822
Philadelphia AthleticsPhiladelphia Athletics1888136434.60981524,8288271,2091838931624303774645,2081,663303.250.305.344.650
Toledo Maumees1890134421.51568644,5757391,15215210824512486715,1321,592284.252.333.348.681
New York GiantsNew York Giants1887129415.55368554,5168161,2591679348651361473264,9241,756308.279.339.389.727
Boston Reds1890130412.62881484,6269921,3062237654772652434355,3211,843353.282.376.398.774
Brooklyn GroomsBrooklyn Grooms1892158409.61795595,4859351,43918310530719629545086,1681,922318.262.344.350.694
Brooklyn GraysBrooklyn Grays1887138409.44860744,9139041,2812008225689456513575,4201,720307.261.330.350.680
Baltimore OriolesBaltimore Orioles1897136401.69290404,8729641,5842436619821724371152555,4962,016328.325.394.414.808
Brooklyn BridegroomsBrooklyn Bridegrooms1889140389.67993444,8159951,2651887947761550494015,4141,752314.263.344.364.708
Chicago White StockingsChicago White Stockings1887127382.58771504,3508131,1771789880655407204004,7771,791356.271.336.412.747
Boston BeaneatersBoston Beaneaters1887127373.50461604,5318341,2551859453649340373924,9081,787332.277.333.394.727
Baltimore OriolesBaltimore Orioles1899152364.58186625,0738271,5092047117649944181223815,7071,906292.297.365.376.741
Philadelphia QuakersPhiladelphia Quakers1887128355.61075484,6309011,2692138947702385523465,0671,801349.274.337.389.726
Cleveland Spiders1887133355.29839924,6497291,1701787714562375464865,0701,544269.252.314.332.646
Columbus Solons1890140353.59079554,7418311,2251597716620545465,3321,586252.258.341.335.675
Cleveland Spiders1888135353.37950824,6036511,0761285912475315795614,9971,358199.234.294.295.589
Cincinnati RedsCincinnati Reds1896128350.60677504,3607831,2832047320648127382422264,9111,693297.294.357.388.745
Indianapolis Hoosiers1888136350.37050854,6236031,1001803334427236434924,9021,448247.238.281.313.595
Brooklyn BridegroomsBrooklyn Bridegrooms1890129349.66786434,4198841,1661847543691517413614,9771,629302.264.346.369.715
New York GiantsNew York Giants1911154347.64799545,0067561,39922510341651160530855065,7811,953369.279.358.390.748
StatMuse has team, season-level data for stolen bases going back to the 1886 season.