Do I owe HST if I stop renting out my basement apartment and start using it personally?

It depends mainly on whether you were claiming input tax credits related to the basement apartment's rental use, and what kind of personal use you're switching to. Converting from a taxable use, most commonly short-term rental, where input tax credits might have been claimed, to purely personal, exempt use can trigger the Excise Tax Act's change-of-use rules, potentially requiring a self-assessment of HST on the relevant portion of the property's value at that point.

If the basement was rented long-term, though, long-term residential rental is itself generally an exempt activity for GST/HST purposes, meaning you likely weren't claiming input tax credits on it in the first place, and stopping that rental to use the space personally is less likely to trigger a change-of-use HST consequence, since you're moving between two activities that were both largely outside the taxable system to begin with.

Because the outcome depends heavily on exactly how the space was being used, whether any input tax credits were claimed along the way, and what "personal use" actually means in your situation, don't assume either way, confirm the correct treatment with a tax advisor, particularly if the space was ever used for short-term rental or if you claimed any input tax credits related to it.