Hank Aaron had the most games with >0 home runs, with 692 games.

Interpreted as:

most regular-season games with 3 more hr by a player

	NAME	G	HR	AB	R	H	2B	3B	RBI	BB	HBP	SO	SB	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Hank Aaron H. Aaron	692	755	2,771	1,026	1,256	102	12	1,425	301	8	240	41	11	3,106	3,647	869	1	25	67	48	.453	.504	1.316	1.820
2	Barry Bonds B. Bonds	687	762	2,452	1,075	1,191	112	17	1,344	574	18	289	113	26	3,062	3,623	891	0	18	149	41	.486	.582	1.478	2.060
3	Babe Ruth B. Ruth	640	714	2,387	1,087	1,200	117	31	1,437	544	5	271	32		2,966	3,521	862	30				.503	.596	1.475	2.071
4	Albert Pujols A. Pujols	634	703	2,515	943	1,146	112	3	1,300	272	24	249	22	10	2,831	3,373	818	0	20	84	72	.456	.509	1.341	1.851
5	Alex Rodriguez A. Rodriguez	629	696	2,543	993	1,175	95	7	1,315	298	37	425	72	16	2,906	3,372	798	2	26	31	51	.462	.520	1.326	1.846
6	Willie Mays W. Mays	593	660	2,362	919	1,107	82	16	1,161	267	10	215	66	29	2,657	3,201	758	2	16	34	37	.469	.521	1.355	1.876
7	Ken Griffey Jr. K. Griffey Jr.	573	630	2,263	834	1,008	101	4	1,184	289	22	309	36	11	2,594	3,007	735	2	18	66	33	.445	.509	1.329	1.838
8	Jim Thome J. Thome	562	612	2,063	835	948	104	5	1,104	373	8	509	4	4	2,454	2,898	721	0	10	52	25	.460	.542	1.405	1.946
9	Rafael Palmeiro R. Palmeiro	535	569	2,092	742	936	80	9	1,042	263	14	231	19	5	2,389	2,741	658	1	19	31	40	.447	.508	1.310	1.818
10	Sammy Sosa S. Sosa	534	609	2,142	798	982	84	10	1,139	230	7	426	31	26	2,393	2,913	703	2	12	41	36	.458	.510	1.360	1.870
11	Frank Robinson F. Robinson	531	586	2,054	819	969	81	16	1,078	254	34	236	37	11	2,366	2,840	683	5	19	42	39	.472	.532	1.383	1.915
12	Harmon Killebrew H. Killebrew	526	573	1,927	724	843	41	1	1,060	323	14	305	2	6	2,276	2,605	615	0	12	32	53	.437	.518	1.352	1.870
13	Reggie Jackson R. Jackson	519	563	1,997	713	886	86	7	1,049	235	18	382	36	18	2,261	2,675	656	3	8	24	30	.444	.504	1.340	1.844
14	Mark McGwire M. McGwire	511	583	1,874	737	830	59	2	1,049	356	14	360	2	1	2,255	2,642	644	0	11	64	29	.443	.532	1.410	1.942
15	Mike Schmidt M. Schmidt	500	548	1,886	715	839	80	12	1,020	289	15	299	32	20	2,207	2,587	640	1	16	49	32	.445	.518	1.372	1.890
16	Manny Ramirez M. Ramirez	499	555	1,913	774	936	108	5	1,134	270	17	329	8	7	2,225	2,719	668	1	24	44	38	.489	.550	1.421	1.971
17	David Ortiz D. Ortiz	490	541	1,910	704	893	104	4	1,024	260	9	258	1	0	2,193	2,628	649	0	14	57	42	.468	.530	1.376	1.906
18	Mickey Mantle M. Mantle	489	536	1,829	736	862	58	11	966	316	3	287	32	6	2,154	2,550	605	1	5	27	25	.471	.549	1.394	1.943
19	Frank Thomas F. Thomas	486	521	1,853	704	856	83	3	989	306	17	255	6	4	2,203	2,508	607	0	27	34	32	.462	.535	1.353	1.889
20	Ted Williams T. Williams	481	521	1,755	763	878	77	12	1,070	437	8	123	3	2	2,203	2,542	610	0	3	26	35	.500	.601	1.448	2.049
21	Jimmie Foxx J. Foxx	477	534	1,832	775	908	89	21	1,126	329	1	213	15		2,174	2,641	644	12			9	.496	.573	1.442	2.014
22	Willie McCovey W. McCovey	474	521	1,709	648	778	48	4	966	252	14	247	8	5	1,987	2,397	573	0	12	67	22	.455	.525	1.403	1.928
23	Gary Sheffield G. Sheffield	471	509	1,802	711	857	77	4	985	286	16	170	42	19	2,125	2,469	590	3	18	35	31	.476	.546	1.370	1.916
24	Eddie Murray E. Murray	470	504	1,875	655	845	62	3	971	205	2	198	15	7	2,093	2,425	569	1	10	33	37	.451	.503	1.293	1.796
25	Miguel Cabrera M. Cabrera	466	511	1,872	695	929	110	2	992	194	9	268	4	6	2,090	2,576	623	0	15	51	48	.496	.542	1.376	1.918