This is definitely a must-see when visiting Montreal. There's a five dollar entrance fee unless you're there to actually attend Mass, but it is worth it.
Free 20-minute tours are held every 30 minutes in French and English, which are definitely worth staying for to get the history of not just the Basilica itself, but also how it ties into the history of the city of Montreal. One is also afforded the opportunity to gain perspective/meaning on the different features of the Basilica (the significance of the stained glass windows, the meaning of the bronze sculpture at the front of the chapel (which is behind the main church), the purpose of the single spiral staircase on the left side of the main church, what "Notre-Dame" even means, etc etc etc...).
In three words: Just do it.
p.s. The Notre-Dame Basilica is a French parish, so for those non-Francophone Catholics that are visiting and considering attending Mass, be aware that all Masses are conducted in French.