It's not essential by any means, but I LOVE mine. Whereas it used to take me an hour to construct a simple skirt hand-sewing, I can now finish one off in about 20 minutes if I really want to. I found mine on sale in Poundstretcher for £30, reduced from £50, and it's served me very well. It's a simple 10 stitch one with a pedal, light and back-stitch button, and it does jam occasionally (it's not a big fan of some of my older vintage threads unfortunately) but we get along fine most of the time.
Visible on the table just above, I couldn't stress more the importance of having good scissors. They needn't be expensive, I think mine only cost about £3, but if you only use them for fabric and thread cutting then you'll notice they work so much better than a pair used for cutting everything. Keep them sharp and clean and your life will be so much easier.
BUY ONE. I know it seems silly since surely you can just pull a seam apart with scissors and careful fingers, but seriously. You will be amazed at how much time it saves, plus they're usually included in most good sewing kits anyway.
Standard dressmakers chalk is wonderful stuff, and certainly cheap enough to buy off eBay or from haberdashery stores. I have a pack of 12 in various colours that cost £2 off Amazon, and it's probably going to last me forever. However my #1 recommendation of this whole list is the little beauty on the right-hand side there. It's called a chalk wheel and it's basically a little pinwheel attached to a pen-like device that when you run it over a piece of fabric, distributes chalk evenly in a clear, solid line. I find it so much easier than pencils or triangles for tracing patterns and it saves me so much time.
Ah, pins. I have a definite love-hate relationship with them. Eternally useful for a million different things, I can't help but resent the fact that no matter how hard I try to make sure they're all accounted for, they always seem to end up on the floor, or the bed, or hiding casually inside a finished seam ready to jab into your skin as soon as you put on whatever you've made. A thimble is also a worthwhile investment, I can't count how many times I've stabbed myself in the fingers when working with difficult or tough fabric.
Useful for a number of different things, such as gathering initial body measurements, checking pattern sizes, designing your own pieces and of course, finding out such essential information as 'How big is my head?' and 'Are my eyes further apart than the average persons according to the internet?'. I have 3 currently because I always seem to be losing them. I'd like to buy a nice one when I have some money, there's loads around with cute patterns and nice cases.
And that is actually it! I have other things in my kit, but none that I use as often as these few items listed here. As you can see, it's easy to build up your own collection of sewing tools cheaply and easily, which you can then use again and again to make anything you like!