I can log in via Safari on my iPhone, or using any other app on any other device, so what's happened with the iPhone?
I've tried uninstalling and reinstalling apps, installing and trying Twitter apps I've never even used before and same problem.
I know it's the correct username and password, as I pasted the same password into Safari as I'm doing with the apps. I've rebooted the phone, checked the Connections access on my Twitter account - all looks good.
Any help gratefully received!
And no, you don't get extra points for pointing out how stupid I'm being :)
Update: Now resolved, thanks to Michele (see comments below) - it was my timezone setting!