IE is made up of multiple componens. Many of which are used in the OS itself to display help and information in several dialog boxes. (Note that FF/Mozilla are now designed this way as well).
So you can get rid of the IE UI but not the MSHTML rendering engine which is in use "privately" but the OS as well as MANY third parties.
My Computer
Computer Manufacturer/Model Number
Scratch built
OS
Windows 7 x64 Ultimate
CPU
i7 960
Motherboard
Asus P6X58D
Memory
12 Gig Corsair Dominator
Graphics Card(s)
Nvidia 480
Sound Card
Maudio Delta 44 + breakout box
Monitor(s) Displays
Dell UltraSharp U2410 24in and Samsung 21 dual monitors
IE is more than just a browser. Many applications like Word, Outlook, etc (those that depend on HTML rendering) need IE in order to function. As Derek said, best you can do is disable it. And if Windows Update comes out with any IE updates, best to install it just in case it fixes something relating to the HTML function or a security issue.
keep internet explorer - you won't regret it, and you don't have to use it as a day-to-day browser.
as others have said, many other windows and third-party software rely on the ie trident engine, such as steam and winamp, amongst many many others. it saves those programs from having to write their own browser to show webpages.
(@marsmimar outlook and word use their own html rendering engine which is flawed and buggy - if only they would use ie!)
Even if you could completely delete it (which is not possible - see above), what would be your gain other than a few bytes saved on the disk. Where is the point? - or am I missing something?
My Computer
Computer Manufacturer/Model Number
HP, Dell, Gateway, Toshiba - 4 laptops and 2 desktops
Appreciate the slap on the head! I was thinking back to earlier versions of Outlook where an email with extensive CSS that was not readable in Outlook could be opened with IE. (Open the message in Outlook > Other Actions in the Office ribbon > View In Browser.) You'd get a security warning about opening suspect HTML in IE. Then you'd click OK to launch IE. Outlook would save the message to the \Temporary Internet Files\content.outlook\ folder as MIME HTML with an .mht extension, and then launch IE pointing to the saved .mht file.