Note that some of these countries celebrate multiple days related to their independence. I'm probably missing others. There are some real interesting ones in this list.

en.wikipedia.org/wiki/List_of...

Israel (date changes based on Hebrew calendar)
Kyrgyzstan
Latvia
Liberia
Malaysia
Moldova
Mongolia
Morocco
Myanmar
Palestine
Romania
Singapore
South Korea
Timor-Leste
Ukraine
Uruguay
Uzbekistan
Venezuela
Vietnam
Yemen

From what I was able to find we are definitely not the only country to celebrate the day we declared our independence. Others include:

Albania
Argentina
Armenia
Bangladesh
Bolivia
Brazil
Cuba
Czech Republic
Ecuador
Estonia
Finland
Georgia
Ghana
Greece
Guinea-Bissau
Haiti