Uzbekistan is a very touristy place, even if you've never heard of it. This year it got about 1.5 million tourists, most of them French of German, and 99.9% of them on package tours. As a matter of fact, the government so heavily promotes the idea of the package tour that is pretty hard to visit the country independently. We had to get a letter of invitation to get a visa, and that will only be issued with help from an Uzbekistan travel agency. Of course most of those travel agencies want you to book a tour with them, but there are a few (notably Stantours) who cater to backpackers.
Travelling independently is a wonderful way to see the country. The Uzbeks are warm, funny, and lively people, but it is hard to see this if you are in a group of 20. There were many times where we were chatting with a shopkeeper only to see him totally change as a big guided group swept in and out.
The other advantage of travelling independently is that the tour groups travel a very well-worn trail. As soon as you get off it you experience a side of Uzbekistan almost nobody sees. We often got invited to stay with people and join them for tea simply by being away from the tourist hordes.
The Uzbeks are wonderful people and if you like old stuff there is a lot of stuff to see in Uzbekistan. Ditch the guide and do it by yourself! The country has a great rail system and lots of English speakers in the tourist industry and is by far the easiest Central Asian country to travel in. It's well worth three weeks.