Whether it's a tornado, flood, high winds, or a hurricane that causes a tree to go down, there are lots of things to think about. How to clean it up, what to do with all of that wood, and ultimately how to replace it are questions that come to mind.
We lost one tree here in our garden in east-central Massachusetts during hurricane Sandy. It came down across our driveway and somehow landed on our power lines without severing them (we are considering ourselves quite lucky). But now that the power company arborists have come and done the minimum job required to get the tree off the lines, we are stuck with a bit of a mess. Here are some thoughts about cleaning up.
First, if you decide to handle it yourself (i.e. pulling out the chainsaw): please — please be careful. There are plenty of chainsaw safety videos online, and it is worth watching them. Here is one that an arborist friend recommended to me after my husband nearly severed his leg a few years ago fixing another downed tree problem.
Know that having someone else come in to deal with the problem is not going to be cheap, but there are ways to cut costs and perhaps even end up with some nice materials. If you have space, you can often get a price cut if you can deal with the wood yourself. Do you have a wood burning stove? Is the wood burnable (if it is dried)? Maybe you can have the tree chipped and then you can use the chips in your garden or compost pile. Maybe you can burn branches later in the winter — an outdoor firepit might need some fuel. Anything you can do to make lighter work and less to haul away will save dollars and cents.
Our tree came out by the roots, which poses a whole different set of troubles than a tree that broke and fell. The stump, if it is still in the ground, will likely be a problem to work around once the tree is gone. Stump grinding is a great option for getting the stump out of the ground (particularly if it is a large tree). I have found that grinding is priced by the stump and the more you have the cheaper it gets. If you only have a few trees it might be worth combining with neighbors who have also lost trees to get the grinder in together. You will all save money over each of you hiring separately.
If the tree has come out by the roots the best thing to do is to get it cut down to manageable sizes that can be chipped, burned or otherwise used. Do not, as I have seen and heard people do, dig a big hole and bury the stump. In many areas this is illegal as it can pollute groundwater, and it will likely cause sinkholes later.
And finally, if you want or need to replace the tree, make sure you consider why it failed in the first place. Was it a Bradford pear that just split and fell? It is worth knowing that this will likely happen to a future Bradford pear as well. It is a common characteristic of the tree. Many trees have distinct characteristics that might make them terrible choices. Perhaps it fell because it didn't have enough space to grow properly and was subsequently top heavy or straggly. If that is the case, it would be worth opting instead for a smaller tree. Of course, in major storms it is certainly conceivable that a perfectly healthy and perfectly placed tree just came down because of obvious forces of nature, but make sure that is really the reason and that in replacing it, planting conditions haven't changed, making something else a better option.
(Image: Rochelle Greayer)

White Enamel Flatwa...
I must be playing too much ACIII. My first though when seeing that picture was, "I could totally climb that."
If someone has a large property it is best to let the tree decompose. This is what's supposed to happen in nature and ironically soil depletion is part of what's causing global warming, which can cause more severe storms: a vicious cycle. CWD is great for not only the soil but amphibians and invertebrates that our bird friends need for their diets.
ps We're in Western Mass by the way. Hope you all stay safe and warm this winter!
Check your local rules on tree disposal. Not all trees should be cut for firewood, so you can't just assume you can cut it yourself and use it. And it's possible your taxes pay for tree removal so you might as well take advantage of it.
And then there is the debate of what to do about the remaining trees - let them be, top them, or remove them. Our maples are more than three-stories high and loom over our house.
I grew up on 40 acres of woodland with my extended family. My dad and grandfather called that kind of treefall (i.e., the trunk is at an angle from the ground) "a widowmaker." If you attacked the job with a chainsaw, the trunk is going to land on you. So you get the tractor, wrap a chain around the down end and pull until the trunk is horizontal. *Then* you make firewood. Of course, if wires were involved, I'm sure they would have left that part to the experts....
About 15 years ago, SF has a really nasty storm. It was so bad the some of the tress in Golden Gate Park fell and they are HUGE. For bike riders, it was a dream because cars could not drive through..We had the entire park to ourselves. What fun...But I understand no fun if a tree barely misses falling on your house in a storm.
Strong second for getting the neighbors together. We had (collectively) 4 dead/dying trees removed after 1 just missed my house in a terrifying straight-line storm in 2010, plus having several more trimmed. The tree company cut us a VERY good deal, since they only had to bring their equipment in once to work on 5 properties.
Why not have a tree expert come and assess your trees every 5 years. Trees that are rotting from within or have root decay, need to come down before they fall and cause damage. We have taken down several trees and used the wood, if it was good, for our wood burning stove. And always replanted hard wood trees or pines. Never plant trees under power or telephone lines. Here in Ohio they will top or remove any branches that even come close to their lines. It has made for some funny looking trees, but fewer power outages.
Topping is never good for the tree and often leads to weak, diseased trees that fall down later. Any arborist whose first recommendation is topping is not worth hiring. A better option for keeping the tree from blowing down is crown thinning, where certain limbs are removed but the overall shape and structure of the tree is preserved.
I'm glad you mentioned putting care into selecting a replacement tree. Too often landscapers push cheap, fast growing trees and the customers are happy for a few years but then the tree falls apart or falls on their house or causes other problems. Look for a local certified arborist to get a good recommendation for a tree.
I'm in NYC and there were a lot of trees that fell in my neighborhood. I went out and gathered stumps after pros came in and cut them apart. Planning on using them as outdoor tables for next to my fire pit seating! Less mess to clean up and free tables!
If you own a chainsaw, you should own chaps.
Please please please do NOT top your trees. I was a urban forester and this was one of the most common issues that came up. Topping is THE WORST thing you could do to a tree, especially a large one. Any arborist will tell you, don't top a tree. (A tree trimming company on the other hand, may tell you to top it because they don't know about trees and by topping, you're ensuring they'll have more work to do in the future.) It will actually make that tree much more of a hazard than if you leave it to be strong and tall. From that new top will grow a ton of branches called water sprouts, which grow really quickly out of stress and are only attached to the surface layers of the tree. They will get huge and then fall on your house, because they are not strong. So you've just replaced a beautiful strong top, with a ton of stressed out, ugly, weak, branches. That's also a great place for decay to set in. If you are worried about your trees, have an arborist lighten them up by trimming some excess branches. Or take down the whole tree and plant something that doesn't get that tall. NEVER TOP TO MAKE A TREE THE "RIGHT SIZE."
Just FYI-- if a tree comes out by the roots, you can replant in that area much sooner than if you need to grind the stump. If you grind the stump, there will be saw dust left in the hole. That saw dust is great for building soil (long-term), but not for roots. It decomposes at such a high temperature that it can burn a new tree's roots. Plus, it doesn't drain water or have the nutrient composition that soil does, which trees need. Wait at least a year to replant.
Also, make sure to plant high, as the soil will continue to settle and the last thing you want is a tree planted in a soggy hole.