You would be charged the federally collected GST or HST based on the province of destination. (If delivered to a HST province, you would be billed HST, otherwise GST).
You could be billed provincial sales tax, PST if the business (i.e. Newegg) operated in that province to where the shipment is being delivered.
For residents of non-HST provinces, you are technically suppose to pay the provincial tax on the goods received based on the honour system. Expect for anything that is registered / restricted provincially like automobiles, where you will often be required to show proof of ownership / value as part of the (vehicle) registration process.
For a purchase sent to Ontario, you can be assured to be billed HST. (I believe Newegg's Canada business operates in the Greater Toronto Area)
From the Canadian Revenue Agency GST/HST rate
. The left-most column is currently in effect. So 13% for Ontario.