I need to travel from Ontario to Buffalo to have a document notarized, but I do not have a current passport. I am a Canadian citizen with parents from Norway and the UK. What other documents can I use to cross the border?
By Land and Sea (including ferries) - Canadian citizens traveling to the U.S. by land or sea are required to present one of the travel documents listed below, and may generally visit the U.S. for up to six months. CBP will accept: Canadian passport, Enhanced Driver's License/Enhanced Identification Card, NEXUS, FAST/EXPRES and SENTRI enrollment cards.
Presuming you are an Ontario resident and possess a valid driver's license there, short of having a passport, the only option is an enhanced driver's license (http://www.forms.ssb.gov.on.ca/mbs/ssb/forms/ssbforms.nsf/FormDetail?OpenForm&ACT=RDR&TAB=PROFILE&SRCH=&ENV=WWE&TIT=023-05009E&NO=023-05009E).
Other options exist (e.g. the NEXUS card) but you can't get NEXUS without having a passport, and are required to maintain a valid passport.
The best option might be to get a passport, but if you need it quickly (less than a couple of weeks or so), the rush fees are quite high.
You said current passport, does that mean you have an expired one? If so, you can try to cross with it. The American border agents can accept it at their discretion. Unless something's changed since June 2016.
My brother and I were going on a trip to the Air Force museum in Dayton Ohio and the night before he realized his passport was expired. Having read the "at their discretion" part and already having the vacation time booked, we decided it was worth a shot. At the border we handed over our documents and answered the agent's questions. At the end he asked my brother "you know this passport's expired, right?" He explained the situation and the agent let us proceed.