Stuart,
First, I want to say that neither Oracle nor TomorrowNow support JDE on VMware in production environments. Open a support case and see how it goes...
Second, regardless of what I just said, I know of a customer that has been running Xe on VMware ESX Server 3.0.1 (VI3) in production for 4 months now. JDE does in fact work on VMware (Workstation, Server and ESX). However, they have seem major performance fluctuations (batch processes, package builds, security authentication,etc). Because of its virtual nature, sharing JDE on a VMware host with other server/apps causes issues in many areas like disk i/o contention, CPU contention and network bandwidth contention. I've seem all three. The key is putting non demanding VMs alongside JDE. JDE is a resource hog. Also, out of experience, when the ESX host utilization reaches or surpasses 75%, all hell breaks loose! Servers lock up, hang for VERY long periods of time and users start to come at you with pitchforks and other pointy objects, if you know what I mean... After four months, they are still trying to find the right recipe for this newly imposed architecture.
Oh, I almost forgot, trying to hot migrate a JDE VM from one host to another host (a.k.a. VMotion) does not work well with JDE application servers at all. As a side note and not related to their current JDE infrastructure (they use the iSeries for the database server), VMotion has caused many of the customer's SQL Server databases to corrupt. Just something to look out for if you are on SQL Server.
JDE in development and testing environments is acceptable. However, I would not run JDE on VMware in any production environment. Keep in mind that you can only allocate a MAXIMUM of four CPU (vCPUs actually) to your virtual machine. My production experience comes from going from an 8 way physical monster to a 4 way virtual machine, which in turn share CPU cycles with other VMs. You will not get the same performance out of a virtual box than you would with the same configuration from a physical. This is important to understand.
Just my 2 cents CAD.