It seems that crows are the harbingers of trouble and disaster, judging by king Theoden's choice of words, when giving a rather frosty welcome to Gandalf:
'I greet you,' he said, 'and maybe you look for welcome. But truth to tell your welcome is doubtful here, Master Gandalf. You have ever been a herald of woe. Troubles follow you like crows, and ever the oftener the worse. I will not deceive you: when I heard that Shadowfax had come back riderless, I rejoiced at the return of the horse, but still more at the lack of the rider; and when Eomer brought the tidings that you had gone at last to your long home, I did not mourn. But news from afar is seldom sooth. Here you come again! And with you come evils worse than before, as might be expected. Why should I welcome you, Gandalf Stormcrow? Tell me that.'
Harsh words. And Grima echoes:
"..." Why indeed should we welcome you, Master Stormcrow? Lathspell I name you, Ill-news; and ill news is an ill guest they say.' ~LoTR- The Two Towers - Chapter 6 - King of the Golden Hall
So crows considered to be the harbringers of bad news and in general nasty creatures, and not just by the Rohirrim, but also by the dwarves:
“I only wish he was a raven!” said Balin. “I thought you did not like them! You seemed very shy of them, when we came this way before.” "Those were crows! And nasty suspicious-looking creatures at that, and rude as well. You must have heard the ugly names they were calling after us. But the ravens are different. There used to be a great friendship between them and the people of Thor; and they often brought us secret news, and were rewarded with such bright things as they coverted for their dwellings. "They live many a year, and their memories are long, and they hand on their wisdom to their children." ~The Hobbit, chapter 15 - The Gathering of the Clouds
Saruman also uses crows to spy on his adversaries.
Tolkien's writing is inspired by various mythologies in which ravens, crows and also eagles serve as symbols of war and death, but also of wisdom - the Nordic god Odin has two ravens, in the Irish mythology war goddes Badb wreaks havoc as a raven or crow among her enemies, according to the Cornish folklore the spirit of king Arthur entered into a red billed Chough, a member of the crow family and so on.
So why the crows singled out as baddies, getting all the bad bird rep in Middle-earth, while ravens (and eagles) shine as benevolent and helpful creatures?
Could it be that Saruman corrupted them? Or were they always nasty?