500 Home Runs but no MVP.

Second baseman Frankie Frisch and pitcher Lefty Grove won the first modern Most Valuable Player (MVP) awards in 1931.  Both are in the Hall of Fame but neither are among the 25 players who hit 500 home runs (HR), 18 of whom won the MVP award at least once.

Rk	Player	HR	From	To	Age	G	PA	AB	R	H	2B	3B	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	BA	OBP	SLG	OPS	Pos	Tm
1	Barry Bonds	762	1986	2007	21-42	2986	12606	9847	2227	2935	601	77	1996	2558	688	1539	106	4	91	165	514	141	.298	.444	.607	1.051	*78/D9	PIT-SFG
2	Hank Aaron	755	1954	1976	20-42	3298	13941	12364	2174	3771	624	98	2297	1402	293	1383	32	21	121	328	240	73	.305	.374	.555	.928	*9783D/45	MLN-ATL-MIL
3	Babe Ruth	714	1914	1935	19-40	2503	10622	8399	2174	2873	506	136	2220	2062		1330	43	113		2	123	117	.342	.474	.690	1.164	971/83	BOS-NYY-BSN
4	Willie Mays	660	1951	1973	20-42	2992	12496	10881	2062	3283	523	140	1903	1464	192	1526	44	13	91	251	338	103	.302	.384	.557	.941	*8/39675	NYG-SFG-TOT-NYM
5	Alex Rodriguez	647	1994	2012	18-36	2524	11163	9662	1898	2901	512	30	1950	1217	91	2032	167	16	101	235	318	74	.300	.384	.560	.945	*65/D	SEA-TEX-NYY
6	Ken Griffey	630	1989	2010	19-40	2671	11304	9801	1662	2781	524	38	1836	1312	246	1779	81	8	102	199	184	69	.284	.370	.538	.907	*89D/73	SEA-CIN-TOT
7	Jim Thome	612	1991	2012	20-41	2543	10313	8422	1583	2328	451	26	1699	1747	173	2548	69	1	74	165	19	20	.276	.402	.554	.956	3D5	CLE-PHI-CHW-TOT-MIN
8	Sammy Sosa	609	1989	2007	20-38	2354	9896	8813	1475	2408	379	45	1667	929	154	2306	59	17	78	202	234	107	.273	.344	.534	.878	*98D/7	TOT-CHW-CHC-BAL-TEX
9	Frank Robinson	586	1956	1976	20-40	2808	11742	10006	1829	2943	528	72	1812	1420	218	1532	198	17	102	270	204	77	.294	.389	.537	.926	97D38/5	CIN-BAL-LAD-CAL-TOT-CLE
10	Mark McGwire	583	1986	2001	22-37	1874	7660	6187	1167	1626	252	6	1414	1317	150	1596	75	3	78	147	12	8	.263	.394	.588	.982	*3/D59	OAK-TOT-STL
11	Harmon Killebrew	573	1954	1975	18-39	2435	9833	8147	1283	2086	290	24	1584	1559	160	1699	48	0	77	243	19	18	.256	.376	.509	.884	357D/49	WSH-MIN-KCR
12	Rafael Palmeiro	569	1986	2005	21-40	2831	12046	10472	1663	3020	585	38	1835	1353	172	1348	87	15	119	232	97	40	.288	.371	.515	.885	*3D7/98	CHC-TEX-BAL
13	Reggie Jackson	563	1967	1987	21-41	2820	11418	9864	1551	2584	463	49	1702	1375	164	2597	96	13	68	183	228	115	.262	.356	.490	.846	*9D8/7	KCA-OAK-BAL-NYY-CAL
14	Manny Ramirez	555	1993	2011	21-39	2302	9774	8244	1544	2574	547	20	1831	1329	216	1813	109	2	90	243	38	33	.312	.411	.585	.996	79D	CLE-BOS-TOT-LAD-TBR
15	Mike Schmidt	548	1972	1989	22-39	2404	10062	8352	1506	2234	408	59	1595	1507	201	1883	79	16	108	156	174	92	.267	.380	.527	.908	*53/64	PHI
16	Mickey Mantle	536	1951	1968	19-36	2401	9907	8102	1676	2415	344	72	1509	1733	126	1710	13	14	47	113	153	38	.298	.421	.557	.977	*8397/645	NYY
17	Jimmie Foxx	534	1925	1945	17-37	2317	9676	8134	1751	2646	458	125	1922	1452		1311	13	71		69	87	73	.325	.428	.609	1.038	*352/7196	PHA-BOS-TOT-CHC-PHI
18	Frank Thomas	521	1990	2008	22-40	2322	10075	8199	1494	2468	495	12	1704	1667	168	1397	87	0	121	226	32	23	.301	.419	.555	.974	*D3	CHW-OAK-TOR-TOT
19	Willie McCovey	521	1959	1980	21-42	2588	9692	8197	1229	2211	353	46	1555	1345	260	1550	69	5	70	176	26	22	.270	.374	.515	.889	*37/9D	SFG-SDP-TOT
20	Ted Williams	521	1939	1960	20-41	2292	9788	7706	1798	2654	525	71	1839	2021	86	709	39	5	20	197	24	17	.344	.482	.634	1.116	*79/1	BOS
21	Ernie Banks	512	1953	1971	22-40	2528	10394	9421	1305	2583	407	90	1636	763	198	1236	70	45	96	229	50	53	.274	.330	.500	.830	36/57	CHC
22	Eddie Mathews	512	1952	1968	20-36	2391	10100	8537	1509	2315	354	72	1453	1444	107	1487	26	36	58	123	68	39	.271	.376	.509	.885	*53/7	BSN-MLN-ATL-TOT-DET
23	Mel Ott	511	1926	1947	17-38	2730	11348	9456	1859	2876	488	72	1860	1708		896	64	109		82	89		.304	.414	.533	.947	*958/74	NYG
24	Gary Sheffield	509	1988	2009	19-40	2576	10947	9217	1636	2689	467	27	1676	1475	130	1171	135	9	111	235	253	104	.292	.393	.514	.907	975D/63	MIL-SDP-FLA-TOT-LAD-ATL-NYY-DET-NYM
25	Eddie Murray	504	1977	1997	21-41	3026	12817	11336	1627	3255	560	35	1917	1333	222	1516	18	2	128	315	110	43	.287	.359	.476	.836	*3D/57	BAL-LAD-NYM-CLE-TOT
Rk	Player	HR	From	To	Age	G	PA	AB	R	H	2B	3B	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	BA	OBP	SLG	OPS	Pos	Tm

Provided by Baseball-Reference.com: View Play Index Tool Used
Generated 6/7/2013.

These seven never won MVP:
7. Thome 612
10. McGwire 583
12. Palmeiro 569    3,020 Hits
14. Ramirez 555    BA leader in a season
21. Mathews 512
23. Ott 511
24. Sheffield 509
25. Murray 504    3,255 Hits

Mitigating items listed above: 3,000 Hits, batting average (BA) leader in a season.  Still no MVP.

Even for HR hitters, BA helps.  Mantle led in HR four times but was MVP in his seasons with his highest BA:

1956 .353, 52 HR, 130 RBI - triple crown

1957 .365, 34 HR

1962 .321, 30 HR

1961 54 HR second in MVP behind teammate Maris (61 HR)

Mays was MVP twice:

1954 .345 (led NL), 41 HR

1965 52 HR

1955 51 HR fourth in MVP behind Campanella, Snider, Banks