@Noah, here's the Keller method, mentioned above. (Sorry if linking to it seems lazy, but I hate re-typing what has already been done!)
http://www.bonappetit.com/recipes/2012/04/the-perfect-poach
The best poached egg I've ever had wasn't really a poached egg in the technical sense. It was a slow cooked egg called onsen tamago (hot spring egg... it's also mentioned in the Momofuku cookbook). I learned the technique online on youtube. Runnyrunny999 has the easiest technique (with one pot and some cornstarch): http://www.youtube.com/watch?v=zzuwiZLIAKY but Jay del Corro has a more comprehensive explanation of what it is and how it's done (he's also fluent in English, for those who might struggle to understand Runny's charmingly garbled English): http://www.youtube.com/watch?v=IZE4cCncih8
When I first tried to poach eggs--last year, actually--I read several sets of instructions on how to do it. I think it was Julia Child who said to create a whirlpool in the pot by stirring the water and then drop the egg into the funnel of the whirlpool. The movement of the water helps keep the egg together.
I take a similar approach to Maedl's suggestion, but I call it the Keller method because that's how I learned it. I break the egg into a ramekin and cover it with white vinegar for 5 minutes. Meanwhile I bring the the cooking water to a steady simmer. Now for the whirlpool; using a wooden spoon I make a vortex in the middle and then slide the egg in and cook for exactly 2 minutes. The combination of the vinegar bath and the whirlpool will give you a perfect egg with its albumen bundled around it and not fanning out all over the place.
Trena's answer is very good, except 3" seems a bit excessive and will add to the issue of the egg spreading. The #1 factor in poaching pretty eggs is FRESHNESS. The older the egg, the more the membranes deteriorate. Also, you can always trim away any wispy bits that you find unsightly.
If you're using fresh eggs but are still unsatisfied with the shape of the cooked egg, then place the egg in a greased ramekin; put the ramekin in simmering water, cover the pan and cook until the egg is done to your liking. I use water to approximately the same depth as the egg. If the egg is stuck despite the greasing, I use a silicon scraper (a.k.a., spatula) to loosen it. HTH, GL
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http://www.bonappetit.com/recipes/2012/04/the-perfect-poach
If you're using fresh eggs but are still unsatisfied with the shape of the cooked egg, then place the egg in a greased ramekin; put the ramekin in simmering water, cover the pan and cook until the egg is done to your liking. I use water to approximately the same depth as the egg. If the egg is stuck despite the greasing, I use a silicon scraper (a.k.a., spatula) to loosen it. HTH, GL
In the link above for Amanda's video, the "reader comments" are helpful.
Amanda’s video, in the Features section of this site:
http://food52.com/blog/3180-perfect-poached-eggs
And lots of other advice in a Hotline thread on this site:
http://food52.com/hotline/7037-a-question-about-a-recipe-simple-perfect-poached-eggs