A sewing machine (I have more than one, from basic to advanced)
Scissors: at least two pairs, one for fabric and one for paper and sewing patterns
A seam ripper
Thread spools in the main colors you use
A measuring tape. Most use inches on one side and cms on the other.
A tailor's chalk or a craftwork pencil
Pins and plastic clips
Sewing needles for your sewing machine or for hand sewing
A thimble (I personally don't use one, except for embroidery)
A set of safety pins (different sizes)
Buttonhole foot for your sewing machine (it's usually provided with the sewing machine and each one has a system)
A steam iron always close by!
To make your life easier
A rotary cutter (and preferably 2, one for paper and one for fabric)
Trimming or needlework scissors
A tracing wheel
A colored "carbon" or "chacopy" paper to transfer sewing lines on the fabric
A cutting mat
A 60cm hard metal ruler
Weights to hold fabrics while you cut (or use any heavy object)
A pin punch to create holes but and gently press through fabric when you reverse
it
A zipper foot for your sewing machine
A sleeve board
And last, for sewing addicts:
Special feet for your sewing machine. I recommend a hem foot, a gathering foot, a conveyor, it's easier for knitted fabrics.
A serger/overlock! I love my Pfaff Overlock 4.0 even if putting threads drives me crazy. But in the U.S. you'll be more likely to have a Singer or Brother.
