I get Awstats and Webalizer with my web hosting account and I find that neither is accurate or very useful. The reported numbers are inflated by up to 1000%, because the tools don't properly identify bots and spiders. Here is a comparison of the Visits metric between three tools over the past 3 weeks (I think Awstats has only partial data for 3/23, and no data for today 3/24, which is why I did not include the numbers).
                            Google  Woopra  Awstats
Sunday, March 1, 2009           10      11      69
Monday, March 2, 2009           13      14      85
Tuesday, March 3, 2009          13      14      96
Wednesday, March 4, 2009        21      28      91
Thursday, March 5, 2009         19      25     107
Friday, March 6, 2009           12      10      88
Saturday, March 7, 2009         12      14     100
Sunday, March 8, 2009           10      11      65
Monday, March 9, 2009           13      14      78
Tuesday, March 10, 2009         17      13      96
Wednesday, March 11, 2009       18      16      87
Thursday, March 12, 2009        19      18      87
Friday, March 13, 2009          12      13      66
Saturday, March 14, 2009        11       7      52
Sunday, March 15, 2009          11      12      57
Monday, March 16, 2009          13      15      92
Tuesday, March 17, 2009         24      22     102
Wednesday, March 18, 2009       18      16      79
Thursday, March 19, 2009        17      18      73
Friday, March 20, 2009          16      11      70
Saturday, March 21, 2009        24      26      67
Sunday, March 22, 2009         103     114     216
Monday, March 23, 2009         232     223     117
I personally prefer Woopra over Google. While it is still in Beta, it can take a long time for your site to get approved, and it will probably be a paid service at some point, the real-time monitoring capabilities are amazing. The new custom reporting capabilities on Google Analytics are superior to Woopra, though. Woopra does not have any capabilties to produce printed reports