Can someone please explain the major differences between Scala, Groovy and Clojure. I know each of these compiles to run on the JVM but I'd like a simple comparison between them.
They can be differentiated with where they are coming from or which developers they're targeting mainly.
Groovy is a bit like scripting version of Java. Long time Java programmers feel at home when building agile applications backed by big architectures. Groovy on Grails is, as the name suggests similar to the Rails framework. For people who don't want to bother with Java's verbosity all the time.
Scala is an object oriented and functional programming language and Ruby or Python programmers may feel more closer to this one. It employs quite a lot of common good ideas found in these programming languages.
Clojure is a dialect of the Lisp programming language so Lisp, Scheme or Haskell developers may feel at home while developing with this language.
Obviously, the syntax are completely different (Groovy is closest to Java), but I suppose that is not what you are asking for.
If you are interested in using them to script a Java application, Scala is probably not a good choice, as there is no easy way to evaluate it from Java, whereas Groovy is especially suited for that purpose.
Groovy is a dynamically typed scripting language, whose syntax is very close to Java. It's good for fast prototyping, scripts, and learning dynamic languages without having to learn a new syntax (assuming you know Java).
Clojure is a dialect of Lisp with a few advanced features like Software Transactional Memory. If you like Lisp and would like to use something like it under the JVM, Clojure is for you. It's possibly the most functional JVM language, and certainly the most famous one. Also, it has a stronger emphasis on immutability than other Lisp dialects, which takes it closer to the heart of functional language enthusiasts.
Scala is a fully Object Oriented language, more so than Java, with one of the most advanced type systems available on non-research languages, and certainly the most advanced type system on the JVM. It also combines many concepts and features of functional languages, without compromising the object orientation, but its compromise on functional language characteristics put off some enthusiasts of the latter.
While Groovy has good acceptance and a strong web framework in Grails, I personally think it is a language with limited utility, particularly as Jython and JRuby start making inroads on the JVM-land, compared to the others.
Clojure, even discounting some very interesting features, has a strong appeal just by being a Lisp dialect on JVM. It might limit its popularity, granted, but I expect it will have loyal community around it for a long time.
Scala can compete directly with Java, and give it a run for its money on almost all aspects. It can't compete in popularity at the moment, of course, and the lack of a strong corporate backing may hinder its acceptance on corporate environments. It's also a much more dynamic language than Java, in the sense that the language evolve. From the perspective of the language, that's a good thing. From the perspective of users who plan on having thousands of lines of code written on it, not so.
As a final disclosure, I'm very familiar with Scala, and only acquainted with the other two.
Scala
Scala evolved out of a pure functional language known as Funnel (http://lamp.epfl.ch/funnel/) and represents a clean-room implementation of almost all Java's syntax, differing only where a clear improvement could be made or where it would compromise the functional nature of the language. Such differences include singleton objects instead of static methods, and type inference.
Much of this was based on Martin Odersky's prior work with the Pizza language (http://pizzacompiler.sourceforge.net/). The OO/FP integration goes far beyond mere closures and has led to the language being described as post-functional.
Despite this, it's the closest to Java in many ways. Mainly due to a combination of OO support and static typing, but also due to a explicit goal in the language design that it should integrate very tightly with Java.
Groovy
Groovy explicitly tackles two of Java's biggest criticisms by: a. being dynamically typed, which removes a lot of boilerplate; b. adding closures to the language. It's perhaps syntactically closest to Java, not offering some of the richer functional constructs that clojure and Scala provide, but still offering a definite evolutionary improvement - especially for writing script-syle programs.
Groovy has the strongest commercial backing of the three languages, mostly via springsource.
Clojure
Clojure is a pure functional language in the LISP family, it's also dynamically typed.
Features such as STM support give it some of the best out-of-the-box concurrency support, whereas Scala requires a 3rd-party library such as Akka to duplicate this.
Syntactically, it's also the furthest of the three languages from typical Java code.
I also have to disclose that I'm most acquainted with Scala :)