Essentially, greed simply means the urge to want more, more than one’s desire. Aren’t we doing the same thing i.e. wanting more when we trail our stops? Trading psychologist say greed is bad, on the contrary successful traders say ride your winners. Whom should one listen to?
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Having a pre-defined Stop Loss is the most essential virtue of successful traders. I know its difficult to overcome greed, but gradually we can develop this habit. I have lost lakhs of rupees by adjusting my stop loss for my trades. So its my advise not to do so. Another option is to hedge your position with Puts or Calls instead of booking loss, if you are lucky enough you can exit break even or even with small profit.
Trialing Stop Loss is always good, IMO. It secures your profits.
But not having a Predefined Target, is a bad idea as far as Tech Analysis is concerned. The money you invest today will appreciate in value, but at what time frame, in few days, in a month, in a year. You should have a predefined target which could reach in a day or few days or so. Once reached you should wind up and put your money on something else which seems good for you (based on your analysis) Even after your wind up, the share might even appreciate further. But remember all shares rise and fall.
I am so sorry @snehil2010, I framed the question wrong. I meant no pre defined TARGETS and not pre-defined exits(which means both stop and target). I have reframed the question, you may want to look into it again. thanks
Ok 
Anyways AastroGuru already answered your question perfectly