Sigh. This old chestnut.
Dresden, Leipzig and Chemnitz were all regarded as legitimate military targets by the political establishment (Churchill in particular). Dresden in particular was a transport hub for the region. The Western Allies wanted to hamper the German retreat from the Eastern front so as to prevent reinforcements reaching the Western front, but it was about more than that.
It was also stated at the time that the raids were intended to help the progress of the Red Army, but I think it was more about demonstrating the power and destructive force of the RAF and USAAF bombing forces to the advancing Russians, as relations between the US/UK and USSR were already going cold by this stage of the war, and there was a certain amount of sabre-rattling from each side to see who would dominate the post-war period.
Please also don't forget that the USAAF were full and willing participants of the Dresden raid; they bombed the city the morning after the RAF raid. Also, it is often forgotten that the USAAF conducted a prolonged conventional bombing campaign against Japanese cities using incendiaries to create large fires; Indeed, these conventional raids caused far more damage and loss of life than the two atomic bomb raids.
As TheMightyTen says, it was Total War. Yes, in hindsight it looks bad and it probably wasn't wholly necessary in the context of defeating Germany, but the target was recommended by Churchill himself as a legitimate target. I doubt that the Germans would have thought twice about such a raid had they had the means; London had been under sustained attack by both the V-1 and V2 'terror' weapons since D-Day.
The loss of life was terrible, no two ways about it. What is also bad is the way the brave men of Bomber Command were 'hung out to dry' by Churchill after the raid, when he realised that history would judge this raid very harshly and sought to distance himself from it. These brave men risked their lives every time they flew over Germany, flying at night with minimal navigation aids (often using star navigation) against sophisticated and well organised defenders, including lots of night-fighters and 88mm AAA. The loss rate was often over 15%.
Regardless of what some people (and historians) might say, the strategic bombing campaign was a second front against Germany for years before D-Day. It wasn't capable of winning the war on its' own as Harris claimed, but it had real effects on German production output, and also in terms of tying up German troops, planes and artillery defending the homeland rather than being used at the front-line. The German 88mm gun was a potent tank-killer on the Eastern front, but hundreds were tied up defending German cities and factories.