I won't mention anything new - Christmas, New Year, Easter, 1st of May, Mother's day, Father's day, Independence day (in our country we have two different dates, one on 16th February and another on 11th March), Coronation day.
From most countries we have one difference - All Saint's day on 1th of November. On this day we visit cemetery and remember our family members, relatives and friends who passed away.
I would say that Christmas, New Year and Easter is most important days in my country.
From what i've heard, Easter is quite big in Russia. I supposed it's pretty big in religious communities in Finland too, but not that big of a deal. Christmas however must be the biggest, and it's celebrated by non-religious as well. We used to have a law keeping all shops closed in Christmas day, but these days they are allowed to be open, most of them are not though.
Right after that is New Years day, which OP didn't even mention, in here it's celebrated by everyone.
Then there are Vappu (may day), which is traditionally celebrating worker's rights with parades and university students. Eve of may day involves heavy drinking and partying, next day marches and picnics.
Independence Day, for general public is celebrated quite quietly. In their own homes, there are some ceremonies obviously and change to feel all patriotic But mostly everyone has their own traditions for that. Like watching the movie "unknown soldier" from tv and independence day reception by president of Finland. Speeches and such.
And my personal favourite is Juhannus. Most people are staying awake whole night as sun doesn't set and people are dancing, burning bonfires, drinking and swimming, usually in their own cabins and bathing in their own saunas. Cities are quite empty and silent in Juhannus.
Seems that some things in Finland is close to my country. We also have holiday on 1st May, but I wouldn't say that people celebrate it much, they more spend like usual weekend.
And Midsummet is quite big thing in Lithuania too. Here it's called Joninės or John's Day in English and celebrations here is very similar.