* Formal: The new shopping mall will encroach on the city's green space, eliminating a beloved park.
* Informal: My neighbor's overgrown hedges are starting to encroach on my property.
* Figurative: The rising tide of technology is encroaching on traditional forms of communication.
* With a negative connotation: The government's policies encroach on individual liberties.
* With a neutral connotation: The expanding suburbs encroach on the surrounding wilderness.
Let me know if you'd like more examples!