If our neighbor dumped his back fill on our property and knocked down some of our trees, what can we do?

You can sue your neighbor for nuisance.  Nuisance is the serious and unreasonable interference with your use and enjoyment of your property.  Damages (monetary compensation you are seeking in a lawsuit) for nuisance would be an inadequate remedy because land is unique and recoveing damages would still leave you with the mess to clean up and the damage to the property to be restored.  When damages are inadequate, you can seek an injunction which is an equitable remedy.  The injunction would require your neighbor to remove the mess he dumped on your property and to restore the damage to the property, the trees, etc. that he caused.

A court will balance the benefits and burdens to the parties in determining whether or not to grant an injunction.  The benefit to you of having your neighbor's mess removed from your property and the restoration of the trees would be balanced against the burden to your neighbor of the cost of the clean-up and restoration of your property.  The court may grant a temporary restraining order which would be in effect until a preliminary hearing at which time the court will determine whether to issue a preliminary injunction which would be in effect until trial at which time the court will determine whether to issue a permanent injunction.

You could have sued your neighbor for trespass which is the volitional entry on to the land of another without consent or legal privilege.  Damages (monetary compensation) would be the remedy, but it would be an inadequate remedy because it would leave you to clean up the mess dumped on your property by your neighbor and it would also leave you with the restoration of your property.  Again, that is why damages are inadequate and an injunction would be the preferred approach in your case.