LR4 -> Edit -> Presets -> Show Lightroom Presets Folder -> double-click into what is highlighted -> Lightroom Settings -> Develop Presets -> Lightroom Presets: Delete or move most things in it. 

I find the General Zeroed Presets useful to undo a bunch of presets, easily, or to just mouse-over and compare to what I have currently applied.

You can't delete the inbuilt presets.

Even if you find the folder where the inbuilt presets are stored and delete them, they will still be there next time you start Lr.

To find the Lr inbuilt presets folder: Go to Preferences and uncheck the box <Store presets with catalog>. You don't have to close Lr - just click <Show Presets folder> and you will be taken to the inbuilt presets folder. Don't forget to check the box again when you are done.

I have my presets stored with my catalog, too, and the place I said was where they are for me, but perhaps they are a slightly different place for you.  Unfortunately, as others have said, even if you delete the *.lrtemplate files in the Develop Presets folder wherever you find it and the multiple copies of it LR have made of it, LR still holds these templates inside of itself and you cannot delete them without modifying the executable or its resources—not something I’d attempt, now that the presets are rolled up in 7 subfolders so you don’t have to scroll more than a page like used to happen.

Paul E wrote:

 

they are taking up valuable screen real estate.

They are not taking up that much real estate - it's seven lines of text when you collapse them.

LR isn't meant to be infinitely customizable.

One workaround I've used. Rename the User Presets folder to something that starts with a letter before "L".

I named my User Presets Folder "A Presets" and now it shows up at the top of the list. This won't solve the quick develop order, but atleast they will show up at the top of the list in the develop module.

PS they take up screen real estate for me as well. I would like to delete them forever.