Latitude is not necessarily a good indicator of a similar climate, eg The British Isles - Same latitude as Newfoundland yet tempatures rarely go below -5 C - much warmer than newfoundlands -15 approx. Ocean currents are the main influence here.
What Countries Have Similar Climates?
Well I think america and Birmingham have the same climate
Most any where you go in the world you will find a place with similar climates. I live in Arizona and from the people I know that did service in Iraq they say it is similar! Of course they have camel spiders and we have black widows and tarantulas. England is a lot like the North Eastern States as is the South of France and Italy a lot like California. Since you don't state where you live or what your looking for get a globe and spin it from where you want to be and go around the world in the same line and it should be pretty much as you would like it to be.