Interesting data and presentation by Pew Research, here.
There’s a button at the top that lets you choose between “Favorable” and “Unfavorable” and one that lets you zoom into a particular year and see the rankings by country, toggling between favorable and unfavorable.
My take is that from 2002 from now our favorability in most countries went down substantially in the 2002->2007 time period, then back up, since. YMMV.