Power Armors are really useful in Fallout 4, since they have an attack power hugely increased in comparison with your regular character's and also have much better defenses. You are provided with a power armor at the beginning of the game and you can even customize it, but you might also be willing to search for more of them, and more powerful, throughout the wasteland.
There are four power armor types: T-45, T-51, T-60 and X-01, obviously each is equipped with increasingly better attack and defense skills. Chances to find them really depend on your character level: if you are level 5, you will probably find a T-45, if you are level 50 chances are you will get a T-60 or a X-01 armor, and even then you will have a randomic component specifically determining which is going to be your power armor and in which spot of the map.
Generally, each power armor you will find on your path will have fusion cores installed so, in case you already own that specific PA and don't want to grab it for any reason, you can also get some fusion cores which are actually pretty expensive, use them for your power armor or selling them.
Of course, you can also grab a power armor and leave it in a specific zone of the map where you want to have a power armor always ready for you to use in emergency cases, or try and upgrade them in a different way in comparison with your “main” power armor. It's really up to you.
Some of the power armors you will find on your path, especially those with the highest level of quality, will require an upgraded Hacker perk for Advanced and Expert terminals. So choose wisely where and how you go before you just waste a lot of time searching for something you couldn't be able to achieve. Also, watch out from enemies: you can go wherever you want theorically in any point of the game, but going in certain places before you have enough skills could be really dangerous.
Take a look, finally, at the video below to have a better idea of where you can easily find 12 power armors spread throughout the wasteland in Fallout 4.
You can check out our Fallout 4 Wikipage showcasing more how to guides, tips and tricks, locations of all collectibles and many other things.