There are zillions of tools out there, many of them super specialized, but these are some basic tools everyone should have around, even if you're not suoer handy.
Sections
3
Indoor
Outdoor
Safety
Indoor
If you’re only going to have one tool at home this would be the one. Tons of uses around the house.
Cordless Drill
Great for cleaning up the garage, the car, or around any project a shop vac is very handy to have around.
Shop-Vac
I mean, it's right there in the name; it has tons of utility. Breaking down boxes, cutting or slicing through whatever you need, all kinds of uses.
Utility Knife
Doesn't get any more basic, or essential, than a claw hammer.
Claw hammer
Essential for any demo project and many other uses.
Wrecking bar/pry bar
A good extension cord will cost a bit more but it's worth having one that's usable outdoors and in bad weather. Be sure to think about what length(s) you need.
Heavy Duty Extension Cord
If you're going to hang anything on your walls you'll need one of these bad boys.
Stud finder
Every DIY project needs a level to keep things straight.
Level
Hard to do almost anything around the house without one of these.
Tape Measure
You'll probably want a few different wrenches, but if you can only have one a large adjustable is a great choice.
Adjustable Wrench
There are tons of socket sets and specialty sockets but a nice basic set serve most of your home needs.
Socket set
Outdoor
Everyone with a yard needs at least a basic rake. Or more than one since different rakes have different uses.
Rake
Got to attack the yard with these once in a while or you'll be overgrown in no time.
Hedge trimmers/clippers
Handy for both outdoor and the garage. I like the battery powered one, it's “grab and go” with no fuel or extension cord to worry about.
Battery Handheld Leaf Blower
The most basic outdoor tool, essential for any gardening or landscaping project.
Shovel
Safety
Have to have it when doing any dusty home improvement projects.
Dust mask
Basic work gloves are essential for protecting your hands. Keep a few pairs around.