If any of the trees in your yard are hazardous, you need to have them removed immediately, including having the stump taken out. But, how do you know which trees are hazardous? If there are no visible signs like half the tree hanging by a strip of bark over your roof, how do you know? You would need to get the tree inspected by a tree service or arborist to fully know, but that's worth it because a number of situations can make a tree hazardous even when the tree looks outwardly fine.
Is It Dead? It's Hazardous
Dead trees are hazardous. You might think it's obvious that a dead tree that's about to fall over is hazardous. But, dead trees often don't look bad. They look old, and if they died from a pathogen or infestation, they can look pretty gnarly. However, they aren't always falling down and don't have these stereotypical signs that the tree made the transition from old/sick to dead. Look for a lack of spring leaf growth and/or the appearance of mushrooms on the trunk. Have a tree service evaluate the tree immediately if you see those. Dead trees can rot from the inside out, meaning that when that tree is hollow and ready to fall, it might look fine on the outside.
It's a Non-native Tree With Shallow Roots in a Windy or Stormy Region
Tree root systems can be shallow, with roots spread out near the surface of the soil, or they can be taproots that extend deep into the ground. Shallow roots aren't that good at holding the tree upright in strong winds, especially in saturated soil that is turning to loose mud in a strong storm. Trees that are native to your area should have root systems that are better at dealing with local conditions, but a non-native tree might not be. If you have trees that are not native to the area and that are known for toppling in wind, remove those and plant a native sapling in its place.
It's From a Highly Flammable Species, and You're in a High-Danger Zone
Some trees produce a lot of oil, and that oil is flammable. If you live in an area where fire is a regular concern, have a tree service identify flammable trees in your yard. Some you might already know about, such as eucalyptus, but other species can be highly flammable, too. Yes, other trees can catch fire, but if they don't produce highly flammable oils, they're a better choice.
Contact a tree service to determine if a tree is hazardous and needs to be removed. If the tree is protected for any reason (e.g., the city considers it a heritage tree, or it's a rare species), the service can help you get permission to remove it.
For more information about hazardous tree removal, contact a local company.