Rickey Henderson had the most games when stealing >0 bases, with 1,035 games.

Interpreted as:

most regular-season games with multiple stolen bases by a player

	NAME	G	SB	AB	R	H	2B	3B	HR	RBI	BB	HBP	SO	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Rickey Henderson R. Henderson	1,035	1,406	3,718	1,139	1,341	199	24	88	416	1,034	43	478	123	4,824	1,852	311	8	21	23	53	.361	.502	.498	1.000
2	Lou Brock L. Brock	755	938	3,093	730	1,209	142	41	33	279	315	25	420	102	3,461	1,532	216	17	11	44	37	.391	.450	.495	.945
3	Ty Cobb T. Cobb	639	820	2,469	725	1,139	144	65	24		367	29			2,931	1,485	233	66				.461	.536	.601	1.137
4	Tim Raines T. Raines	631	808	2,375	625	965	116	28	45	297	484	17	208	38	2,905	1,272	189	11	18	50	33	.406	.507	.536	1.042
5	Max Carey M. Carey	605	740	2,306	603	897	102	38	10		379	32	149		2,783	1,105	150	66				.389	.481	.479	.961
6	Eddie Collins E. Collins	603	740	2,184	593	909	101	40	14		470	24			2,774	1,132	155	96				.416	.524	.518	1.042
7	Joe Morgan J. Morgan	578	689	2,018	554	736	89	23	66	272	587	13	177	36	2,640	1,069	178	6	16	12	21	.365	.507	.530	1.037
8	Willie Wilson W. Wilson	572	668	2,250	525	878	74	36	11	211	182	20	255	31	2,481	1,057	121	15	14	12	22	.390	.438	.470	.908
9	Bert Campaneris B. Campaneris	528	648	2,086	471	759	80	25	16	160	228	23	245	35	2,386	937	121	36	13	5	13	.364	.430	.449	.879
10	Vince Coleman V. Coleman	526	752	2,158	503	761	75	40	10	166	262	6	325	73	2,450	946	125	17	7	1	16	.353	.423	.438	.861
11	Juan Pierre J. Pierre	502	614	2,034	451	809	77	24	7	189	169	43	102	43	2,304	955	108	50	8	1	20	.398	.453	.470	.922
12	Ozzie Smith O. Smith	496	580	1,873	407	708	78	17	6	204	309	6	87	25	2,244	838	101	44	12	18	21	.378	.465	.447	.912
13	Brett Butler B. Butler	492	558	1,849	443	683	63	24	5	150	346	9	154	47	2,249	809	92	36	9	7	9	.369	.469	.438	.907
14	Kenny Lofton K. Lofton	491	622	1,955	562	781	98	33	25	197	310	11	189	42	2,303	1,020	156	14	13	15	20	.399	.481	.522	1.003
15	Otis Nixon O. Nixon	485	620	1,638	451	592	45	10	3	126	278	2	203	61	1,945	666	58	17	10	3	15	.361	.452	.407	.859
16	Maury Wills M. Wills	460	586	1,945	420	755	49	15	3	139	180	10	150	47	2,176	843	67	32	9	11	29	.388	.441	.433	.874
17	Cesar Cedeno C. Cedeno	457	550	1,717	394	653	102	10	50	261	241	24	164	43	2,000	925	162	6	12	23	33	.380	.460	.539	.999
18	Barry Bonds B. Bonds	455	514	1,551	460	610	103	9	113	360	503	19	202	19	2,091	1,070	225	2	16	84	17	.393	.542	.690	1.232
19	Paul Molitor P. Molitor	445	504	1,793	444	731	108	13	37	241	269	11	176	21	2,096	976	158	13	10	16	20	.408	.485	.544	1.030
20	Davey Lopes D. Lopes	445	557	1,646	415	569	51	15	33	167	342	10	202	26	2,037	749	99	23	16	6	28	.346	.457	.455	.912
21	Luis Aparicio L. Aparicio	439	505	1,794	402	627	58	12	17	172	202	6	104	26	2,032	760	87	17	13	8	25	.349	.414	.424	.838
22	Jose Reyes J. Reyes	430	517	1,810	441	715	107	36	36	209	219	2	168	25	2,050	1,002	179	10	9	21	14	.395	.459	.554	1.012
23	Ichiro Suzuki I. Suzuki	422	509	1,782	404	762	76	12	20	143	172	10	134	23	1,972	922	108	4	4	48	16	.428	.480	.517	.997
24	Roberto Alomar R. Alomar	413	474	1,612	388	637	104	12	32	252	256	13	166	24	1,917	861	148	22	14	15	25	.395	.478	.534	1.012
25	Jimmy Rollins J. Rollins	406	470	1,698	346	647	100	22	30	196	226	7	196	21	1,945	881	152	5	9	12	11	.381	.454	.519	.972