Each side had its full share of strategists good and bad, and some who passed from the scene too early to evaluate. Some of them also excelled at strategy but failed at the tactical and/or operational level, so success may not have always followed their strategic ideas.
As author of the strategy which ultimately won the war, U.S. Grant would have to be at or near the top of the list. Rising from Col to Lt Gen and General in Chief, his was one of the more meteoric ascents during the war. Grant recognized the need for coordinated efforts against the Confederate forces in the field. He saw that the Confederate armies, rather than territory and points on a map, were the main targets, but also appreciated the value of cities and supply lines. Even before he was in overall command, Grant had wanted to take out Mobile. In VA Charlottesville and Lynchburg - both important rail centers - were favorite objectives of his. After Sherman had captured Atlanta Grant sent him gentle reminders that Hood's army not Atlanta was his objective. Few other commanders realized that concentration in time and concentration in space were the true recipes for victory.
Winfield Scott deserves mention here for his "Anaconda Plan," although it had the early war fascination with Richmond as the overall objective. The blockade and control of the Mississippi River were the strongest points of Scott's plan. However, given his advanced age and debilitating size by 1861 his best days were long behind him.
George McClellan was one of the rising stars of the antebellum army and knew more than anyone else in the country, possibly the planet, about siege warfare. For all his tactical faults and shortcomings as commander of a field army, McClellan was a brilliant military mind, one who could dominate a chess board when the human elements were removed from it. The idea behind the Peninsula Campaign - if not the execution of it - was superb, as was his idea to reduce Richmond by siege once he finally got there. Little Mac had an appreciation, matched perhaps only by Joe Johnston, for securing one's base fully and making sure all one's military ducks were in a row, so to speak, before committing to battle. Had McClellan been in a European-style staff role, or remained behind a desk overseeing movements on a map rather than being in direct command of a field army, he would be remembered much more kindly by history.
William Rosecrans is one of the unsung heroes of the Western Theater. His biggest achievement was gaining Chattanooga w/o a fight, and had arguably been the brains behind McClellan's West VA Campaign at the outset of the war. Unfortunately Rosecrans' defeat and his personal retreat from the battlefield at Chickamauga permanently blemish an otherwise stellar record as strategist and tactician. (I have always wondered by Rosey was never given a chance in the Eastern Theater.)
William Sherman, Philip Sheridan and John Pope all had an appreciation for "total war" that few other commanders did. Pope brought it out too early - in the days when their was still the early 19th century romance about the war and such actions were vilified. Sherman and Sheridan both recognized how the home front was also a military front and how to best eliminate it militarily.
Robert E Lee was the best that the Confederacy had to offer. Like McClellan, Lee had an engineering background and an appreciation for terrain that few could rival. Lee realized that the Confederacy was outnumbered and could never have any realisitic hopes for numerical parity on the battlefields, and with that understanding knew how to compensate and make best use of what he had - even if it meant undertaking high-risk operations. Lee also argued - usually in vain - for the shifting of troops from quiet theaters to concentration in active theaters: troops were of no value sitting idle in garrisons. He was a rumored candidate for Secy of War in 1862 and several months before the end of the war was finally named General in Chief.
GT Beauregard was another of the proponents of troop concentration, as long as it didn't entail taking troops from him only giving them to him. He seemingly constantly bombarded Davis and the War Dept w/grandiose proposals to strip most of the Confederacy of troops for grand offensives, of course under his command. But Beauregard certainly had his off-days as well.
John Bell Hood - most folks would say that he belongs in the other column of this list, but that would be based on results not the idea. If McClellan's results are overlooked to the benefit of his planning, Hood should be accorded the same favor. Aggressive by nature, Hood observed from his service in Lee's ANV how to be aggressive to greatest advantage. Hood inherited the Army of Tennessee w/his back against a wall - the similarities to Lee's assumption of command of the ANV could not have been lost upon him. As Lee took the offensive against McClellan, so too would Hood against Sherman. But Sherman was not McClellan, the Army of Tennessee was not the Army of Northern Virginia, and Hood was not Lee. After losing Atlanta Hood employed another REL-esque strategy - falling upon Sherman's supply lines to force Sherman to fall back. Lee had forced Pope (Second Manassas Campaign) and Meade (Bristow Stn Campaign) to retreat using a similar strategy. When Sherman refused to take the bait, Hood (with Beauregard's concurrence) devised another Lee-like plan - to invade Tennessee; if Sherman took Georgia, Hood would take Tennessee, Kentucky and had his eyes on Ohio. Yet Hood's subordinates would fail him outside Atlanta and at Spring Hill, and his own poor tactical choices at Franklin all overshadow Hood's historical reputation.
Now for the not so great...
It would be difficult to find a more disappointing officer in a gray uniform in terms of independent command than James Longstreet. Longstreet was never subtle in his suggestions that he warranted his own command, and he never did anything to prove himself worthy of it; in fact his two stints in independent command proved him completely unworthy of it. Although the Suffolk Campaign was not his idea, he botched it completely and ignored orders to return to the ANV before the opening of the Spring offensive, thus Lee was without two divisions at Chancellorsville. His actions at Chattanooga - although more in the tactical or operational realm than the strategic - contributed greatly to Grant being able to lift the Confederate siege. His insistence on being detached to Knoxville from Chattanooga was extremely flawed, and pouring salt in the wound he botched his Knoxville operation entirely. Bragg needed every soldier he could find at Chattanooga to offset the accessions Rosecrans and then Grant was getting from other armies, yet Longstreet was angry at not being named Bragg's successor so wanted away from him, thus took three divisions to Knoxville and neither commander - Bragg nor Longstreet - had the troops they needed for their own operations. And every time that Longstreet failed he found a scape goat: for Suffolk it was Sam French, for Chattanooga it was Evander Law, for Knoxville it was Lafayette McLaws, and overriding all from Chickamauga onward it was Braxton Bragg.
Perhaps the only officer who rivaled Longstreet as a failure was John Pemberton. There were only a handful of officers who lost their entire army prior to the end of the war - Pemberton reigns supreme in that category. Ostensibly under Joe Johnston's command during the Vicksburg Campaign, Pemberton made a horrible choice for the security of Vicksburg by surrendering the initiative to Grant and withdrawing into his defenses ringing the city while awaiting a relief column. Once exchanged Jeff Davis proposed Pemberton for corps command under Joe Johnston but eventually realized that would come close to causing a mutiny, thus Pemberton - once a Lt Gen - became a Lt Col in command of the heavy arty in Richmond's defenses.
Speaking of Jefferson Davis, his cordon defense strategy and his insistence on being his own General in Chief until the war's end gives him high ranking on this list as well. Davis' penchant for playing favorites and holding grudges, regardless of the military consequences of his personal friendships and vendettas, was unforgivable and in the end quite costly.
Ambrose Burnside simply was in over his head once he got stars. His initial plan to go around Lee via Fredericksburg was sound but when his pontoons were late in arriving his decision to await them although the surprise of the move was lost shows a lack of creativity. The disaster of the Battle of Fredericksburg falls under tactical failures, so he will not be faulted for that here. But his "Mud March" was a combination of bad luck and another example of his inability to adapt his plans to unforeseen circumstances. The move itself was very similar to what Joe Hooker would do several months later. Sent back West after Fredericksburg Burnside languished at Knoxville, only entering the pages of history again there b/c Longstreet's failures to dislodge him. A final tick mark against Burnside is his handling of the Crater attack. He gets kudos for the creativity of the mine idea, but allowing fate/luck to put his worst division commander in the van of the attack that very well could have taken Petersburg, well, is in line with what one would expect from the man whose plan for renewing the attack at Fredericksburg consisted of personally leading the IX Corps into the meat grinder of Maryes Hgts.
Ben Butler is representative of the many political generals who donned Union blue. Unfortunately for the Union war effort, he was near the top of the seniority list. Butler managed to make himself the most hated man in the entire South, and a good portion of the North as well. His handling of the escaped slaves at Fort Monroe created a political hot potato for the Lincoln administration. He followed this up by insulting the female population of New Orleans - and by extension nearly the entire population of the South - while in command of that city. Fast forward to 1864 and his command of the Army of the James, he very nearly captured Richmond and then took his army out of the fight by bottling his army up at Bermuda Hundred. A final note on Butler's failures was his attempt to literally blow up Ft Fisher outside Wilmington with a "powder ship" which caused a lot of noise and fireworks and hardly gained notice from the Confederate garrison.