How does Parrot compare to other virtual machines?
Parrot is the virtual machine originally designed for Perl 6.
There are now two VMs originally designed for Perl 6; commits to MoarVM began in 2012.
What technical capabilities does the Parrot VM offer that competing virtual machines such as the Java Virtual Machine (JVM)/Hotspot VM and Common Language Runtime (CLR) lack?
In another answer on this page, Reini Urban, the current (April 2015) Parrot lead dev, provides a brief comparison of Parrot with the JVM and CLR VM.
According to Reini, a key advantage Parrot has over MoarVM is "effectively lock-less threads".
The following answer was written in 2009. See also this 2015 update by raiph.
To expand on @Reed and point out some highlights, Parrot's opcodes are at a far higher level than most virtual machines. For example, while most machines store integers and floats, the basic registers are integers, numbers, strings and Parrot Magic Cookies (PMCs). Just having strings built in is a step up from the JVM.
More interesting is the PMC, sort of like JVM's object type but far more fungible. PMCs are a container for all the other more complicated types you need in a real language like arrays, tables, trees, iterators, I/O etc. The PMC and the wide variety of built in ops for it means less work for the language writer. Parrot does not shy away from the messy but necessary bits of implementing a language.
My information may be out of date, but I believe opcodes are pluggable, you can ship a Parrot VM that only contains the opcodes your language needs. They were also going to be inheritable, if your language wants their arrays to work a little different from stock Parrot arrays you can do that subclass it.
Finally, Parrot can be written for not just in assembler (PASM) but also a slightly higher level language, Parrot Intermediate Representation (PIR). PIR has loops, subroutines, localized variables and some basic math and comparison ops, all the basics people expect in a programming language, without getting too far away from the metal.
All in all, Parrot is very friendly to language designers (it is written by and for them) who want to design a language and leave as much of the implementation as possible to somebody else.
You can read about much of this on the Parrot VM Intro page.
The main advantage Parrot has over the JVM or the CLR would be that it is designed to support dynamic languages first, and potentially provide better support and performance for dynamically typed languages. The JVM and the CLR are both geared more towards supporting statically typed languages, and many of the design decisions show that.