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http://onemansblog.com/2007/03/26/how-id-hack-your-weak-passwords/

Very informative article on how easily weak passwords are broken.

This table from the article should be fairly convincing as to why you would want very good passwords:

Password Length All Characters Only Lowercase
3 characters
4 characters
5 characters
6 characters
7 characters
8 characters
9 characters
10 characters
11 characters
12 characters
13 characters
14 characters
0.86 seconds
1.36 minutes
2.15 hours
8.51 days
2.21 years
2.10 centuries
20 millennia
1,899 millennia
180,365 millennia
17,184,705 millennia
1,627,797,068 millennia
154,640,721,434 millennia
0.02 seconds
.046 seconds
11.9 seconds
5.15 minutes
2.23 hours
2.42 days
2.07 months
4.48 years
1.16 centuries
3.03 millennia
78.7 millennia
2,046 millennia

Source (and the entire article, recommended reading)
http://onemansblog.com/2007/03/26/how-id-hack-your-weak-passwords/

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