StatCounter is a perfectly reputable organisation, and I certainly haven't heard of them using spyware. If they did, the word would soon get about, and they would have no business. They make their money from the advertisers you see on the StatCounter page that you login to when you want to view your stats.
Plenty of good web hosts have excellent stat software running on their servers, and often they'll turn it on for site at no charge, or for a token charge. It does the same analysis as the StatCounter software, but the information is on your own server - it's worth asking.