General:
* Intrude
* Invade
* Encroach
* Violate
* Infringe
* Interfere
More specific:
* Trespass (legal term)
* Burglary (illegal entry with intent to commit a crime)
* Breaking and entering (illegal entry into a building)
* Poaching (illegal hunting or fishing)
* Squatting (occupying property without permission)
* Overrun (to enter and occupy in large numbers)
The best synonym will depend on the specific situation you're describing. For example, if you're talking about someone walking across your property without permission, "intrude" might be a good choice. If you're talking about someone breaking into your house, "burglary" would be more accurate.