Do I have a legal right to lateral support from my neighbour's land if their excavation causes my ground to shift?

Yes, in general. Ontario recognizes a basic common-law right of lateral support, meaning your land is entitled to the support it would naturally have received from your neighbour's adjoining land in its undisturbed, natural state. If a neighbour's excavation, digging a new foundation or basement close to the boundary, for example, removes that natural support and causes your land to subside, shift, or crack, the neighbour who did the excavating can potentially be held liable for the resulting damage.

The nuance worth understanding is that this right traditionally protects land in its natural state; support specifically for the added weight of buildings and structures isn't automatically guaranteed to the same degree unless there's some additional basis for it, such as a specific easement of support. In practice, though, courts recognize that excavation causing genuine damage to a neighbouring property is a serious matter, and a neighbour planning significant excavation near a shared boundary is expected to take reasonable precautions, shoring, engineering assessment, and advance notice, to avoid causing that kind of harm.

If you're facing significant excavation next door, or if you're the one planning it, get an engineering assessment and legal advice early, since prevention is far more manageable than a damage claim after the fact.