First, ESXi will run using SATA drives in AHCI mode connected directly to a motherboard that uses an Intel ICH7 or ICH9 chipset, but NOT an ICH8 or ICH10.

VMWare will use as much RAM as you can give it. RAM is more important then CPU.

Having said that, a multicore CPU is really helpful. ecspecially if you plan on using the software iSCSI initiator.

Use an Intel Pro 100 or Pro 1000 NIC. NIC support is pretty bare in ESXi, so just hop on newegg and spend 20 bucks on one.

We have two options, the first and cheapest is to use a motherboard based on the ICH7 or ICH9 chipset. ESXi will support SATA drives in AHCI mode connected to this chipset,so an ICH7/9 board, a few gig of RAM, a SATA drive and an Intel NIC will have you on your feet.  If you have this kind of setup, all you’re going to need to do is boot off of the ESXi installer CD and you’ll be done a short time later.

The second option is a bit more involved, but will work on ICH8 and ICH10 motherboards. I personally run an ICH10 based board with a quad core and 8 gig of RAM using this method.  This method also requires iSCSI storage to be available. I use Solaris and ZFS for my SAN. So, if you have an ICH8 or ICH10 motherboard, you need to create a USB bootable thumbdrive and install ESXi onto that. You can follow these simple instructions for linux or you can google for instructions for windows. Once you have your boot drive created, you will need to give your host an IP and use the management console to setup iscsi storage.  Have fun!

Updated for ESXi  3.5 update 4
This is ridiculously cool.  I have a quad core motherboard with 8 gig of RAM that won’t install VMWare ESXi (it’s an ICH8 board and only ICH7 and ICH9 will work), but I’ve been hearing that you can install ESXi onto a thumbdrive and run it on boards that wouldn’t work otherwise.  Most instructions are for windows and, being the windows dude that I am, I decided to tweak it for linux.  First, you’ll need a linux box and a 1 gig or larger USB drive.  Download the ESXi ISO and then mount it in linux like so

mount -t iso9660 -o loop VMware-VMvisor-InstallerCD-3.5.0_Update_4-153875.i386.iso /mnt/esx

Now we’re going to write the installer file to the thumbdrive. I’m assuming the thumbdrive is /dev/sdb

tar xvzf /mnt/esx/install.tgz usr/lib/vmware/installer/VMware-VMvisor-big-3.5.0_Update_4-153875.i386.dd.bz2 -O | bzip2 -d -c | dd of=/dev/sdb

This will take a little bit, but once it’s done you’re good to go. pop that drive into a USB boot capable board, configure iSCSI storage and emulate away!