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