Q:

How to suppress missing javadoc checkstyle warning on enum constants/values? 

Checkstyle is complaining about enum values not having an attached javadoc comment.   But at least in many of my enums, since the values themselves are often self-explanatory, adding javadoc simply seems to reduce readability with unneeded clutter.   Consider the following examples:
/**
 * Example enum to illustrate the problem.   Each value of this
 * enum represents a day of the week. 
 */
public enum DaysOfWeekClean {

    SUNDAY,
    MONDAY,
    TUESDAY,
    WEDNESDAY,
    THURSDAY,
    FRIDAY,
    SATURDAY;

}

/**
 * Example enum to illustrate the problem.   Each value of this
 * enum represents a day of the week, with comments added to each
 * distinct value to make the point. 
 */
public enum DaysOfWeekCluttered {

    /**
     * The day of the week named "Sunday". 
     */
    SUNDAY,

    /**
     * The day of the week named "Monday". 
     */
    MONDAY,

    /**
     * The day of the week named "Tuesday". 
     */
    TUESDAY,

    /**
     * The day of the week named "Wednesday". 
     */
    WEDNESDAY,

    /**
     * The day of the week named "Thursday". 
     */
    THURSDAY,

    /**
     * The day of the week named "Friday". 
     */
    FRIDAY,

    /**
     * The day of the week named "Saturday". 
     */
    SATURDAY;

}

If the JavadocVariable module is added to my checks, the first example (DaysOfWeekClean) will be flagged, while the second example (DaysOfWeekDirty) will pass. 
And that leaves me in a bit of a dilemma.   I want checkstyle to flag normal class members/variables which are not commented, but to leave my enum constants alone.   After quite a bit of searching through the Checkstyle documentation (and the Checkstyle source code itself) and several StackOverflow questions, I can't seem to figure out how to set this up. 
I can warn when javadoc is missing from both enum constants and class members/variables or I can ignore both, but I can't seem to check one and not the other. 

For reference, here are some checkstyle configurations which I have tried, and their results:

Simple declaration which warns when both a class member or enum constant has no javadoc:
<module name="JavadocVariable" />

Declaration which warns when either a class member or enum constant has no javadoc:
<module name="JavadocVariable">
    <property name="tokens" value="VARIABLE_DEF" />
</module>

Declaration which FAILS to warn when either a class member or enum constant has no javadoc:
<module name="JavadocVariable">
    <property name="tokens" value="ENUM_CONSTANT_DEF" />
</module>

A:

In order to skip enum values, you can configure the check like this:
<module name="JavadocVariable">
  <property name="tokens" value="VARIABLE_DEF"/>
</module>

The documentation as of 2017-01-18 is missing this information, but this is planned to be fixed. 
I tested this behavior with Eclipse-CS 6.14, so if it does not work for you anymore, that would be a bug. 

A:

You can suppress CheckStyle warnings with either the SuppressionCommentFilter, or from Checkstyle 5.7 by using the @SuppressWarnings annotation. 
You'll need to do some setup of your checkstyle.xml configuration. 
By Comments
Add the SuppressionCommentFilter to your checkstyle.xml:
<module name="SuppressionCommentFilter"/>

Then add comments to your code to checkstyle off & back on. 
//CHECKSTYLE:OFF
public enum DaysOfWeek {
    //..
//CHECKSTYLE:ON

By Annotations
If you prefer annotations, you can use the SuppressWarningsFilter.  Note that it needs the SuppressWarningsHolder module.  Add both these modules to the TreeWalker in your checkstyle.xml:
<module name="TreeWalker">
    <!--  make @SuppressWarnings annotations available to Checkstyle, and filter warnings by annotation
    -->
    <module name="SuppressWarningsHolder" />
    <module name="SuppressWarningsFilter" />
</module>

Now you can annotate your enums with the warning you wish to exclude.  Use the appropriate warning code & checkstyle should suppress it. 
@SuppressWarnings("checkstyle:<appropriate warning here>")
public enum DaysOfWeek {
    //..

References:

http://checkstyle.sourceforge.net/config_filters.html#SuppressionCommentFilter
http://checkstyle.sourceforge.net/config_filters.html#SuppressWarningsFilter
https://stackoverflow.com/a/4023351/768795
https://stackoverflow.com/a/22556386/768795

