I used to think that estimating another website's traffic was impossible if one did not have access to its raw data.
I noticed several free online services ready to suggest numbers. I took some time to check them and their data. I found the data results to be 3 times as high as the lowest data for a given URL. This was quite frustrating. Pretty useless and unreliable.
Fortunately, after a lot of research, I found compete.com which has a solid source of real user data. It provides a good statistical estimation of unique visitors per month. The only drawback is that it only focuses on U.S. population. But, it is still a very good start (probably the best estimator).
Recently, I also found Google's AdPlanner which provides great monthly data in addition to demographic data. It seems like you need a Google account to access it.
For daily page views and unique visitors, I used to found StatShow to be more or less realistic and a bit on the conservative side. But, recent tests with some blogs I own now show completely false and unrealistic results. It is out of my list.
If you know a free online tool which is more reliable, please put a comment and I will add the link to this post.
More free online web tools (best of) here.