This is an interesting misconception of US Grant which was propagated by many redemptionists during the turn of the last century (or so argues Joan Waugh, who I happen to agree with). This myth then gained traction the public mind, who has repeated it to the point of wide acceptance.

But I am here to tell you that US Grant was a good general. Nay, a GREAT general! who archetyped American military strategy for the last 150 years, and who invented modern warfare ;). As such we will discuss his two major Campaigns, the 1863 Vicksburg Campaign, and the 1864 Overland Campaign.

So, 1862. In April, 1862, Grant fought a decisive battle with Confederate forces, now known as the Battle of Shiloh. Following his success, Grant was tasked with capturing the City of Vicksburg, which was the last major Confederate strong point on the Mississippi River. In December, 1862, US Grant launch a major attack aimed at taking the city from the south. This was launched in conjunction with an attack on the north of the city, led by William T. Sherman. Grant landed a sizeable force South of the city, and began to move his forces along the rail lines, which all merge at Vicksburg. Unfortunately, Nathanal Bedford Forrest was also operating in the area. Forrest launched several raids into the Union rear positions, which destroyed munitions dumps, trains, broke rails, and cut telegraph communications. Grant rapidly found himself low on supplies, out of reliable communication, and surrounded by a hostile population. He quickly canceled the attack and retreated across the Mississippi. (W. T. Sherman never received the cancellation notice, and launched his offensive on schedule, but with no support. His forces were mauled and he was forced to retreat north. Oops.)

But in 1863, Grant came back. After spending the Winter and Spring preparing for a new offensive, Grant again landed troops south of Vicksburg. But this time, Grant landed them without the encumberance of much of their supplies. The only wagons he brought with him were heavily loaded with munitions. Everything else was found by foraging. (Grant was able to do this logistical miracle by tapping a gifted supply officer, General Phil Sheridan, who had done similar things during the Pea Ridge Campaign). Grant landed his troops, and was quickly opposed by the armies of Pemberton and Johnston (Pemberton manned the garrison, while Johnston fought a dynamic defense). Johnstons forces began engaging Grant almost immediately. But the Confederates sought a repeat of the 1862 campaign, where Grants rear areas were ravaged and he was forced to retreat. But Grant had cut his supply line to the Mississippi river, and so there was nothing to be ravaged that wasnt protected by a large army. Johnston lost a tremendous amount of time and energy by trying to cut Grants line of communication, and all the while Grant pushed forward towards Jackson, MS, defeating Confederate details as he went. The Confederates were pushed into Jackson and Johnston's army was smashed. Grant then turned on Pemberton, who had based himself out of Vicksburg and had harassed Grants flank the whole time. Grant hemmed Pemberton into the city, and laid a classic siege of the town. It fell on July 4 1863.

Not only did Grant win a major series of battles and destroy two Confederate armies, but the capture of Vicksburg was a major strategic victory for the Federals. It closed all trans-Mississippi trade for the Confederacy, and freed up Union troops to push even deeper into the South. And it was done thanks to US Grant, who won a truly Napoleonic victory. And he did so on a logistical shoestring! The Corsican would have been proud. We often remember only Robert E Lee as the Napoleon of the New World, and he rightly deserves that title. But the Vicksburg Campaign shows that US Grant was no slouch either.

For my money, Vicksburg is undeniable proof that Grant was a master of maneuver warfare, on the same level as Lee. But then there is the whole sticky business of the Overland Campaign, and the massive casualties sustained therein. But I will argue that the Overland Campaign was a whole different beast, a new and shockingly modern system of warfare which would be more comfortable in 1914, than in 1864. In this new system, both sides will suffer (and the Union will suffer more, it cannot be denied), but I will suggest that it was necessary, it was the best approach to the situation, it conceals an artful campaign of maneuver, and it has inspired American Military thinkers ever since.

The Overland Campaign of 1864 was developed out of the failed invasion of Pennsylvania, culminating in Gettysburg. After the retreat from Gettysburg, the Confederate army occupied positions on the south side of the Rappahannock River, while the Union camped on the North side. After several sideshows in the west (culminating the Battle of Chattanooga), US Grant was given overall command of Union forces. He took over the Army of the Potomac, and only May 4, 1864 he began crossing the Rappahannock and Rapidan River. Lee had set up his base of operations on the other side of the Wilderness, a dense area of forest on the south side of the Rappahannock River. When Lee learned of Grant's movements, he immediately ordered an attack into the Wilderness. After several days confused fighting, Lee was in definate possession of all the major avenues out of the Wilderness towards headed directly towards Richmond. Most Union Generals, once in this position, quickly abandoned the campaign and returned North in defeat (and it should be remembered that the Battle of Chancellorsville was fought on exactly the same ground). But Grant, while defeated tactically, did not accept the traditional strategic implications of that defeat. Where almost every other general would have called himself checked, Grant simply tried a new strategy. Instead of fighting on Lee's terms, Grant would simply continue applying pressure on Lee's exposed flanks. As such, Grant did something that no other Union general had ever done. He turned Lee's flank.

There is far more indeed. First, if we compare casualty rates instead of casualty numbers, we see that Lee sacrificed far more of his army. If Grant was a butcher, Lee was a bigger one.

Grant matured greatly with his independence in the West, where he could learn from his mistakes (and from his impressive victories). He consistently showed a remarkable combination of flexibility and perseverance, which meant that his defeats would not shake him, like they did to so many of his colleagues, but instruct him. When he was surprised and battered after almost being pushed into the river on the first day of Shiloh, he struck back and snatched victory from the jaws of defeat; when an attack at Vicksburg was repulsed or a plan went awry, he pressed on and eventually took the city; when he was bloodied in the Wilderness, he kept moving south, unlike all of his predecessors, and continued the offensive. Grant's persistence was one of his greatest traits. More to your question, however, Grant had high aptitude for strategy, logistics, and maneuver. His ability to maneuver, rather than merely the ability to outnumber, was better demonstrated nowhere than at Vicksburg. Grant could abandon his supply lines when necessary and still have an army in fighting condition. When he finally came East, he was able to coordinate the entire Union war effort and was finally able to turn the army that McClellan had built into an effective fighting force against Lee. He was able to see through the politics and realize that focusing on Lee in the East, not Richmond, was a strategy that would win. But in fighting Lee, he did not just throw his numbers against Lee's but maneuvered around Lee, forcing Lee to move, and waiting for the ideal opportunity to attack. This is not to say that Grant did not take advantage of his numerical superiority (if he didn't, then what type of general would he be?) but it is to say that he did far more as well, making skilled use of maneuver and displaying great logistical acumen and an adept handle of grand strategy. While his reputation has suffered since the years following his death, when the myth that he was merely a butcher gained steam, it has been partially rehabilitated and continues to improve today.

For a recent and generally broad view of Grant's generalship, see the first half of Geoffrey Perret's Ulysses S. Grant: Soldier and President. For a somewhat dated but incredibly important and insightful study, see J. F. C. Fuller's fantastic The Generalship of Ulysses S. Grant. The best study of Grant's Overland Campaign is Gordon Rhea's series of masterful books on the topic. It should dispel any remaining thoughts that Grant was a butcher who relied only on his superior supply of men and materiel. See: The Battle of the Wilderness, May 5-6, 1864; The Battles for Spotsylvania Court House and the Road to Yellow Tavern; To the North Anna River: Grant and Lee, May 13-25, 1864; and Cold Harbor: Grant and Lee, May 26-June 3, 1864.

Edit: I see now that /u/Beondthegrave gave a far more detailed answer but I will leave this up anyway.

That reputation was necessary to sustain the myth of the Lost Cause.

If the South was doomed from the start, then clearly any idiot (or combination thereof) would eventually win. It especially helps that Southerners (propagators of the myth) didn't like Grant's presidency any more than they liked getting beat by him in battle.

Grant was a superb General and in many aspects superior to Lee particularly in strategy where Lee could have been more successful at tactical level at least until he found Grant in his front. I will not repeat what has already been said but I'd like to mention the following often forgotten.

First of all, in the West, prior to come to the Eastern theater as Commander of the Union Forces Grant was a pioneer in experimenting with the combined use of the Navy and the Army to deliver mutual support and using amphibious warfare. The Yazoo River expedition trying to approach and conquer Vicksburg is a good example. He also was one of the first in the Union side to decide to leave his supply train behind and leave off the land. All this talks about his Generalship.

Second. Grant had a strategy as opposed to all his predecessors who, in the East, mainly focus on taking Richmond and would not have much plans after a battle was fought other than retreat to regroup and fight the next one. Grant wanted originally all Union forces to exert pressure at once so the Confederacy would not be able to cover all fronts and would give way somewhere else.

Third. Once in the East the battles became bloodier, no doubt, but it is also true that he was fighting Lee, the most effective Confederate commander and with the troops more harden in battle. But as opposed to his predecessors Grant would not cede after a setback, he'll keep moving against Lee and increasing the pressure on his Army. Eventually both got into a stalemate in Petersbourg but when it fell and then Richmond Grant did not halt at Richmond, in fact did not enter it at all as most Union Generals have dreamed but continued to pursuit Lee's army until it was encircled and forced to surrender at Appomattox.

Yes attrition became part of the game and some of Grant's decisions like the frontal assaults of Cold Harbor are questionable but no doubt he was trying to keep the momentum and he saw an option. I could go on but Grant must be considered one of the finest Generals in the US Army history and as opposed to the 20th Century he was a man that although a product of West Point the curricula of the time was not that remarkable in military terms and he self taught himself much of the job after years living a civil life.

My advice is that you start at the original source and read his memoirs and asked your question to yourself again once you have finished them, I am sure you would have by then perceived his evolution as General.