There is a study at Cnet which looks at how long it will take for an unpatched comp connected to the Internet to get infected:
According to the researchers, an unpatched Windows PC connected to the Internet will last for only about 20 minutes before it's compromised by malware, on average. That figure is down from around 40 minutes, the group's estimate in 2003
If you are wondering why the drop from 40 minutes to 20 minutes is so significant:
The drop from 40 minutes to 20 minutes is worrisome because it means the average "survival time" is not long enough for a user to download the very patches that would protect a PC from Internet threats.
Get the full study here:
Study: Unpatched PCs compromised in 20 minutes
Take Care,
Richard