http://www.orchidboard.com/community...ng-photos.html
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I'm guessing you have a Phalaenopsis ... here's some pix
https://www.google.com/search?q=phal...w=1364&bih=683
If the spike is brown, it won't do anything more, so you can cut it off. If it's green (or part of it green), it's a personal decision to cut or not. You can't harm the plant either way (tho do use sterile cutters on green spikes - you can just use a flame to make sure the cutting instrument is disinfected, or a disposable, unused blade). If the spike is green, but the plant has poor or no roots, cut the spike.
If your orchid is a Phalaenopsis, you may want to read the first few, to several, pages of this thread
http://www.orchidboard.com/community...ends-here.html