The electrification of residential energy demand for heating and transportation is expected to increase peak load and require additional generation and transmission capacities. Electrification also provides an opportunity to increase demand response. With a focus on household electricity consumption, we analyse the contribution of appliances and new services, such as individual heat pumps and electric vehicles, to peak consumption and the need for demand response incentives to reduce the peak. Initially, the paper presents a new model that represents the hourly electricity consumption profile of households in Denmark. The model considers hourly consumption profiles for different household appliances and their contribution to annual household electricity consumption. When applying the model to an official scenario for annual electricity consumption, assuming non-flexible consumption due to a considerable introduction of electric vehicles and individual heat pumps, household consumption is expected to increase considerably, especially peak hour consumption is expected to increase. Next the paper presents results from a new experiment where household customers are given economic and/or environmental incentives to shift consumption to or away from specified hours. The experiment focuses on the present classic consumption and shows that household customers do react to incentives, but today the flexibility of the classic consumption is limited. Considering electric vehicles and individual heat pumps, for an individual household, the consumption of each of these technologies roughly doubles the household's consumption and considerably increases their potential for flexibility. Thus, in order to introduce incentives for demand flexibility, while considering reducing peak consumption, policy makers should initially focus on households that have a heat pump and/or an electric vehicle.