My H-1B start date is in Jan 2015. Can I travel to the US as a visitor (Canadian Citizen) in December, and then reenter the US in January on the H-1B?
In my case, I was Indian citizen at the time in 2006 and was on student visa on Canada and had my Visitor Visa for USA. I got US Student visa and Immigration officer cancelled my US Visitor visa at the time of issuing US Student Visa.
But, as Canadian Citizen you can enter USA and exit it and reenter in January on H1B Visa Stamping to receive H1-B Status so that you can receive your I-94 card and apply for SSN number. As you can not start working before your H1-B Start date and receive any money. Normally they allow you to enter country on set date of stamping on your passport for H1-B Visa.
Hope this information will help you
Citizens of Canada and Bermuda do not require visas to enter the United States as temporary workers; however, a temporary worker petition approved by USCIS is required. For more information see U.S. Embassy Ottawa website, U.S. Consulate Hamilton website and CBP website.
Since you do not need a visa to enter the US as a tourist, nor as a temporary worker, I suspect you can enter the US before your start date. I also wonder why you have an H-1B visa in the first place.