Yom Ha'atzma'Ut - Israel's Independence Day

Yes, It's a Halakhic Holiday

by Rabbi Meshulam Roth, of blessed memory, 
in Responsa "Kol Mevaser" 21. 

A rabbi in Tchernovitz, Galicia, he immigrated to Israel in 1944, 
where he was a member of the Chief Rabbinate.

The fifth day of the month of Iyar was established as a day of 
celebration throughout the land to remember the miracle of our 
salvation and freedom. It is obligatory upon us to celebrate 
it as a festive day and to say Hallel (holiday prayer of rejoicing).  
Even one city, or individuals, who establish a holiday because of 
a miracle that befell them, must keep this practice, they and 
their descendants forever.  This is true even if they move to a 
different city, as is written by Maharam Alshaker (responsa 49),
quoted by Magen Avraham (686,5) and Eliyahu Rabbah, and [endorsed] 
by Hatam Sofer (responsa 191, O.C.) in the case of salvation from 
death… 

Certainly in our case, touching on the entire public of Klal Yisrael, 
when we were redeemed from subjugation to the other nations and 
became a free people with sovereign independence, and we were also 
saved from being killed and destroyed by out enemies - 
certainly it is incumbent upon us to establish this day as 
a holiday.  And those who set this day specifically were correct, 
in that the principle aspect of the miracle in our 
redemption from subjugation to freedom occurred on this day with 
our declaration of independence.