Is it possible to set up a bare-metal hypervisor on my laptop?
Yes, this is a Type 1 hypervisor. Common Type 1 hypervisors include Xen and VMware vSphere Hypervisor (formerly VMware ESXi Single Server). There should be no problem using the partitions as virtual disks for the VMs, but disk image files on a single partition offer greater flexibility, such as the ability to increase the size of the image and apply data compression to the image (on the host file system) to reduce the disk space required. VirtualBox can access partitions directly; I'm not sure about VMware, but it should be able to do the same.
As long as you have the necessary hardware support (and you do), there should not be a problem with setting up a bare-metal hypervisor on your computer. In fact, my old laptop (8 GB memory, quad-core AMD Phenom II (K10 mobile) processor) now runs Microsoft Hyper-V Server 2012 R2, and the VMs get near-native performance.
If you're setting up separate partitions for individual operating systems another option is to set up multiboot with GRUB. This has the advantage of allowing the guest OS to interface with the hardware directly for increased performance and compatibility, and frees you from the idiosyncrasies and individual limitations of the host type 1 Hypervisor.
For example, VMware ESXi does not support windows 8 prior to ESXi 5.0 Patch 4, and would require the installation of a type 2 Hypervisor such as Qemu within a guest OS for ARM-based processor emulation (eg. for Raspberry Pi development). Xen on the other hand can be quite difficult to configure and driver support can be dependant on distribution compatibility.
Furthermore, your type 1 hypervisor may or may not be compatible with laptop power management technologies and drastically affect battery life.
Another option you may consider is to set up a stripped down version of Linux with KVM installed and Intel VT-x (for your Core i7) hardware assisted virtualisation support as a Host OS. Whilst this is not technically a type 1 hypervisor implementation it may offer you the functionality you seek. I would definitely recommend storing your disk images as files, and not partitions if you go down this route - much easier to back up, manage and upgrade/decommission.
This discussion has quite a bit more useful information should you wish to research the topic further.
You may also consider running your prospective type 1 within a type 2 hypervisor such as VMware Workstation, VirtualBox or Qemu to 'try before you buy' and check out interface etc. although it will be difficult to determine performance and compatiblity.
Citrix has recently released type 1 bare-metal hypervizor for desktops - XenClient.
It's free for up to ten users.
Some introductory articles:
http://my-techno-arena.blogspot.com/2014/08/type1-bare-metal-hypervisor-for.html
http://blogs.citrix.com/2010/11/18/xenclient-how-to-p2v-your-existing-os/
Update
XenClient was discontinued and there is no free replacement from Citrix.