Well, I can't say I created many threads (if any), but as far as I recall, I have seen this button.
It is a simple textual link inside a div which adds the background graphics making it standing out, but it should be visible even if the image cannot be loaded.
Is there a pattern in the browsers used by those not seeing it?

I only see the "New Topic" button if I am signed in.     The button is visible with or without the external background image loaded.   I bet its because people are not signed in and cookies are being eaten.   If I close my browser in either IE or Chrome on Windows 7 the site logs me out causing me to not see the "New Topic Button" anymore (even though I knew I signed in 10 minutes ago, but accidentally closed my browser).   I use google apps to sign in.

FYI, you can see where the New Topic button is within this screenshot:

OK, I think we're getting to the bottom of this. From the image you posted Ian, it looks to me like you are signed into Zoho, but you haven't yet joined the Processing Forum. See the blue "Join Now" button beneath the Search box? You need to join the Processing forum before you'll be able to see the New Topic button.