Is there a way to close the lid on a MacBook without putting it sleep?

You most definitely can. It is even documented on Apple Support

tl;dr: Plugging in an using an external keyboard and mouse will wake the device, even if the lid is shut

Apple Portables: How to use your computer in closed clamshell (display closed) mode with an external display

If you are using a wired keyboard and mouse:

• Make sure the computer is plugged in to an outlet using the AC power adapter.
• Connect a USB keyboard and mouse to your computer.
• With the computer turned on connect the Apple portable (using the appropriate Apple adapter if necessary) to the appropriate port on the external display or projector and turn the display or projector on.
• Once your computer's Desktop appears on the external display, close the computer's lid.
• Once the lid is closed, wake the computer up by either clicking your mouse button or by pressing a key on your external keyboard.

You should now be able to use your Apple portable as you normally would, using your USB keyboard and mouse.

The process is a little bit different if you are using a wireless keyboard and mouse. To check that out, or and further details, see Apple Portables: How to use your computer in closed clamshell (display closed) mode with an external display on Apple Support.

Try using InsomniaX.

I researched around and came across a project to keep my MacBook on without having to keep my keyboard or mouse in since I hate having to go get them to plug into my Mac. Here is the project's page https://code.google.com/p/macosx-nosleep-extension/

I did some additional research and found this MacRumors thread.

Actually if you have a keyboard or mouse connected to it, with the PSU connected as well, you can close the laptop wake it back up. The Monitor will become the default screen, and the screen on the laptop stays off.

I haven't confirmed that this works.