Is there still war in between countries?

Answer 1

There is a lot of "peace keeping actions" and undeclared wars occurring but here are the legally declared wars now in effect:
As of 2007, a few declarations of war remain in effect, though they are usually retained for lack of a peace treaty rather than reflecting an active state of hostilities.

North and South Korea have remained legally at war since the Korean War.
Syria has been at war with Israel since the Yom Kippur War.
Having refused to sign the 1949 Armistice Agreements, Iraq has remained in a state of war with Israel ever since.
Armenia and Azerbaijan remain deadlocked on the issue of Nagorno-Karabakh and have yet to find a peaceful resolution.