Stitch quality is dependent on using the correct needle for your thread, fabric and the type of machine sewing you need to do for your project. When the wrong needle is used you may get stitching that puckers, skips or the thread may break.
Fabric
Consider fabric weight, thickness, weave type (woven or knit), weave density (close weave or loose weave) and composition (natural fibre or synthetic).
Thread
Consider matching your thread composition to your fabric (polyester thread for synthetics, cotton for cotton fabrics etc.) and to your sewing purpose (seams, hems, topstitching, quilting, machine embroidery etc.).
After selecting your fabric and thread type the final consideration is the style and size of needle to achieve the best results.
Needle Style
If your project or thread is specialised, choose your needle based on that rather than fabric type e.g. embroidery, quilting and twin needle work have a specific needle, while there is a specific thread for topstitching which requires a certain needle.
If your project involves general sewing or overlocking, base your needle choice on the characteristics of the fabric you are sewing  with. For instance are you working with woven fabrics heavy or light denim jeans, leather, or stretch fabric?
Needle Size
When you have chosen the type of needle you must also choose the size (width) of needle.
Here's a useful guide to use as a reference;
Size 60/8 - Use for very fine synthetic and cotton fabrics.
Size 70/10 - Use for net, chiffon and nylon sheer fabrics.
Size 75/11 - Use for voile, chiffon and organza fabrics.
Size 80/12 - Use for cotton lawn, taffeta, silks and tricot fabrics.
Size 90/14 - Use for poplin, chintz, gingham and synthetic velvet fabrics.
Size 100/16 - Use for cord, denim, gabardine and heavy suiting fabrics.
Size 110/18 - Use for heavy cord, heavy denim, leather fabrics etc.
Size 120/20 - Use for heavy cord, heavy denim, leather fabrics etc.
Sewing Machine Needles are stamped with the needle type and size. The needles are stamped on the curved side of the needle shank with metric and imperial sizes followed by relevant needle mark codes (K0, K1, K2 etc).
Here is some more detailed information about each type of Sewing Machine Needle;
Ideal for most woven fabrics, some knits and synthetics. The Universal Needle has a slight ball point making it extremely versatile. It works well on practically all domestic machines (not industrial machines) and is the most commonly used needle for synthetic woven and natural fibres. The finer needles are generally used on lightweight fabrics and the larger sized needles for medium to heavy weight fabrics. Suitable to be used with polyester, cotton or silk threads.
Available in sizes 60/8, 70/10, 75/11, 80/12, 90/14, 100/1, 110/18 and assorted fine, medium and heavy sizes. Size 80/12 is also available in Titanium super strength needles.
Ideal for cotton knits, interlock, rib knits, fleece, double knit, and most knit fabrics. The tip is more rounded than the Universal needle and is designed to push the fabric fibres apart rather than cutting them, preventing the knit fabric laddering or running after stitching. Generally threads such as polyester or polyester/cotton blends are best. Once again the finer the fabric the finer the needle to be used.
Available in sizes 70/10, 80/12, 90/14 and assorted mix.
Designed especially for two way stretch knits, lycra, power net, silk jersey, spandex and highly elasticised synthetic fabrics, also ideal for sewing elastic. The Stretch Needle has a specially designed scarf which prevents skipped stitches. Threads are usually polyester or cotton wrapped polyester and for extra stretch the woolly nylon threads are suitable.
Available in sizes 75/11, 90/14 and assorted mix.
Ideally suited for denim fabrics, heavy twill, workwear, and other densely woven fabrics such as canvas and heavy linens. Engineered with a very sharp point and a stiffer shank to resist needle deflection and allow penetration of dense fabric. Suitable threads range from synthetic or blends, cotton wrapped polyester, 100% polyester and heavier topstitching threads.
Available in sizes 90/14, 100/1 and assorted mix.
For genuine leather. The leather needle has a cutting point and is used for sewing leather, suedes and difficult to sew projects. It is often referred to as a chisel point needle as the point resembles and acts as a chisel in motion. Do not use with ultra suede, synthetic suede or PU imitation leather.
Available in sizes 90/14, 100/16, 110/18 and assorted mix.
Sharps Needles (Microfibre) (K5)
For silks, micro fiber fabrics and for penetrating densely woven fabrics, also ideal for piercing and quilting layers of cotton fabrics with batting. A strengthened shaft also helps to reduce needle deflections as the needle penetrates multiple layers of fabric. The sharp point also produces smooth buttonholes.
Available in sizes 60/8, 70/10, 80/12, 90/14 and assorted mix.
Ideal for piercing and quilting layers of cotton fabrics and batting. A strengthened longer shaft also helps to reduce needle deflections as the needle penetrates multiple layers of fabric while maintaining a perfectly straight stitch.
The embroidery needle is specially designed for machine embroidery using Rayon, Polyester or Cotton machine embroidery threads. This needle features a wider hole to allow the thread to pass freely. Another feature is a pontoon scarf with oversize bump to reduce the chance of skipped stitches which can result when fabric is flexing up and down rapidly with the fast moving embroidery stitch.
Available in sizes 75/11, 90/14 and assorted mix. Size 80/12 is also available in Titanium super strength needles.
Ideal for sewing and embroidery with rayon and metallic threads on woven or knitted fabrics. The Metalfil Needle is designed with a very large eye, allowing the threads to feed freely as you sew without splitting, burning or shredding. This needle is also suitable for general purpose sewing, giving the added advantage of being easier to thread due to the enlarged eye.
The extra large eye accommodates thick topstitching thread. The extra sharp point allows the needle to penetrate easily through all medium - heavy weight fabrics. These needles are best for top stitching, sashiko and blanket stitching.
Available in sizes 80/12 and 90/14.
Twin needles are used for practical sewing and decorative sewing such as pintucks, seam finishes and topstitching etc. The size of the needle is measured in mm from tip to tip (e.g a 2mm needle has a 2mm space between the points). Available in many types and sizes including Universal Twin Needles, Ball Point Twin Needles, Embroidery Twin Needles, Jeans/Denim Twin Needles, Metalfil Twin Needles and Stretch Twin Needles.
The triple needle has 3 needles evenly spread on one shaft. Ideal for heirloom sewing, decorative seams and topstitching. Size indicates distance between needles - 3mm 80/12.
Please Note: Twin and Triple Needles are fixed in a nylon block and should be used at slower speeds and not for prolonged periods.
The single “wing” blade on the side of this needle cuts a narrow hole in the fabric, creating the popular heirloom-style decorative stitching.
Type A (System 16 x 231, DBX1, 2053)
Suitable for these overlocker machines/models;
Pfaff - 793, 794, 795, 796, 797
Brother - B500 & B600 series, M760DE, TE-B505
Elna - All MO series
Husky - M430, M431, M435, M435C, M435D, M436, M440, M441, M530, M535, M535C, M535D
Singer - 10U series. 14U12, 14U13, 14U22, 14U23, 14U32, 14U52
Type B (System DCX1, 81X1)
Suitable for these overlocker machines/models;
Babylock - All BL-3 series, EF-405, EF405M
Janome - 603, 603A
Mammylock - 334, 334D
Pinnock - P1, P2, PBL-1, PBL4, PBL4-436DF, PBL4-543DF
Pfaff - 603, 603A
Type E (System HAXISP)
Suitable for these overlocker machines/models;
Janome - 100, 200, 300, 400, & 500 series
Babylock - SL600, SL700, SL800, All BLE series, Protage 402
Globe - All models
Husky - SL3000 series, 34D
Toyota - SL3400, SL3403
Type G (System 705H, 2020)
Suitable for these overlocker machines/models;
Toyota - 6300, 6600, SL-1, SL-3000, SL-3404, 6500
Janome - All Combi series
Pfaff - 774E, 776E, 783, 784, 785, 786, 787, 788
Bernette - All models (EXCEPT MO203, MO204 & MO205)
Brother - M730, M730D, M760, M760D, all PC, PL, 900 & 9000 series
Elna - All models (EXCEPT MO102, MO103 & MO104)
Husqvarna Huskilock - M460, All M540, 550, 560, 570, 580, 680, 800 & 900 series
Singer - 14U64A, 14U344, 14U354 
Type K (System 16x75, 2054)
Suitable for these overlocker machines/models;
Singer - 14U32 series, 14U34 series, 14U44, 14U65 series, 14U85 series, 14U234 series, 14U285, 14U286, 14U444, 14U454B, 14U544, 14U554, 14U555, 14U594, 14U595 
Here is some other information you may not know about sewing machine needles;
Replacing Needles
Machine needles should be replaced after a maximum sewing time of 8 hours. Replace needles more frequently when sewing synthetic fabric, appliques or machine embroidery. This will avoid skipped stitches, fabric pulls and frayed threads.
Breaking Needles
Machine needles are designed to break for the protection of the sewing machine hook mechanism. If a needle bends, do not sew with it. When a machine needle breaks, it is a warning to check the following;
1) Is the needle type and size correct for the fabric?
2) Is the thread too thick or unsuitable for the needle size and application?
3) Is the upper thread feeding freely?
4) Are the thread tensions set too tight?
5) Does the machine need cleaning?
6) Is the correct presser foot fitted?
7) Is the correct sewing technique being used?
8) Is the fabric being pulled, pushed or dragged during sewing?
9) Twin needles, triple needles and other specialty needles can break due to excessive heat build up. To avoid breakage reduce speeds and avoid prolonged useage.