There are sewing machine needle charts at Sew-it-love-it.com and Sewing.about.com. The former has the needle size in US and European sizes along with the corresponding fabric weight and type, all in one chart.
The US convention for sizing needles grades them according to increasing thickness, from size 8 to 18. A size 8 is a thin needle for fine fabric, and size 18 is a thick needle for heavy fabric, such as canvas. The middle size, 14 is the most commonly used size, and it suits medium-weight fabric. The size of the needle matters, because a thin needle breaks with heavy fabric, and a thick needle makes unsightly holes in fine fabric.
In addition to needle size, seamstresses need to consider what type of needle to use. For general purpose sewing, needles are universal, ball point or microtex. Universal needles can be used with the majority of woven fabrics. Ball point needles are suitable for knits and jerseys, as they preserve the stretch of the knits. Sharp or microtex needles are suitable for fine silks and microfibers with tight weaves.
Speciality needles are available for sewing leather or fabric containing spandex. Needles should be changed with each new project to ensure a sharp tip and even stitches.