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That will be system specific to the user based on screen size and the current size that they have the browser window at. There is no way to tell when a browser is going to cause a horizontal scroll bar (or position indicator as some people are now calling them that alludes the fact that most people have wheel mice now and never use a 'scroll bar' anymore).
You're pretty safe assuming that everyone is at, at least, 800x600 resolution. This basically means that you want to stay under 780 pix width... for both IE and Netscape.
That's about the best you can do since you don't have any control over people making their broswer window smaller (unless you want to really piss them off using the DOM)
Horizontal scroll bars usually cause a rapid use of the back button.
Also, using relative width tables can make your page start looking ugly at higher resolutions depending on your layout.
The last stats I saw showed 16-20% of the net still at 640x400.
I personally consider horizontal scroll bars a forbidden feature on anything I design.
If I have to scroll to view your content, I am not getting the design intent anyway, just parts of it.
It's like wooooo,let me scroll to see the rest of the picture without really seeing the picture as a whole. It makes no sense.
But I agree with you about it being impossible to avoid scrolling completely. There will always be someone out there viewing your page at 640x480 in a really small window :-)
15-20% using 640x480? Where did you read that? I've been hearing under 10% for a few months now and my logs are showing more like 5%.
There hasn't been a new computer shipped any time this year with the resolution set below 800x600.