You can write normal Java servlets in Groovy (i.e. Groovlets).
There is also a GroovyServlet which automatically compile your .groovy source files, turn them into bytecode, load the Class and cache it until you change the source file.
Here's a simple example to show you the kind of thing you can do from a Groovlet.
Notice the use of implicit variables to access the session, output & request.
Or, do the same thing using MarkupBuilder:
Setting up groovylets
Put the following in your web.xml:
Then all the groovy jar files into WEB-INF/lib. (You should only need to put the groovy jar and the asm jar).
Now put the .groovy files in, say, the root directory (i.e. where you would put your html files). The groovy servlet takes care of compiling the .groovy files.
So for example using tomcat you could edit tomcat/conf/server.xml like so:
Then access it with http://localhost:8080/groovy/hello.groovy