Get exception instance class name

Here you go:

try {
    throw new ArithmeticException();
} catch (Exception e) {
    System.out.println( e.getClass().getCanonicalName()); 
}

Output:

java.lang.ArithmeticException 

The type of the exception is shown as part of the output of:

e.printStackTrace();

To get it programmatically you can use:

String exceptionClassName = e.getClass().getName();

It is poor form to have logic depending on exception sub types within a catch block. Sonar will flag this as a code violation (squid S1193).

Instead you should add multiple catch blocks to catch different types of exceptions:

try {
    readFile(fileName);
}
catch (java.io.IOException e) {
    LOG.error("Error accessing file {}", fileName, e);
}
catch (java.lang.IllegalArgumentException e) {
    LOG.error("Invalid file name {}", fileName, e);
}

Note: Since Log4j 2 (and SLF4J 1.6+) you can add a throwable as the last parameter and it will be recognized as such. So the above will work!

Since Java 7 you can also do a multi-catch:

}
catch (java.io.IOException | java.lang.IllegalArgumentException e) {
    LOG.error("Could not read the file {}", fileName, e);
}

The benefit of the multi-catch is that you can handle multiple exception types within a single catch block without having to revert to a common super class (like java.lang.Exception) that would include exception types you didn't want to handle.

Default exception logging is something like

try
{
//
}
catch (Exception e)
{
e.printStackTrace();
}

This will print the stacktrace of the exception to system.err

If you are looking to add some contextual information, you can take a look at Apache Commons ContextedRuntimeException

public static void main(String[] args) {
    try {
        doSomething();
    } catch (ContextedRuntimeException e) {
        System.out.println(e.getMessage());
        System.out.println(e.getContextEntries());
    }
}

private static void doSomething() {
    int divisor = 0;
    int dividend = 100;
    int result;
    try {
        result = dividend / divisor; // Just throw an exception to test things....
        System.out.print("DIVISION RESULT: "+result);
    } catch (ArithmeticException e) {
        throw new ContextedRuntimeException("Oops..division by zero not allowed", e)
        .addContextValue("Divisor", divisor)
        .addContextValue("Dividend", dividend);
    }
}

would output:

Oops..division by zero not allowed
Exception Context:
    [1:Divisor=0]
    [2:Dividend=100]
---------------------------------
[(Divisor,0), (Dividend,100)]

Like @user1438038 said in the comments of this question, you can use e.getClass().getSimpleName() to get the exception name, for example:

try {
    Double x = 1 / 0; // ArithmeticException
}
catch (Exception e) {
    System.out.println(e.getClass().getSimpleName()) // Will print "ArithmeticException"
}

If you want to get java.lang.ArithmeticException (to follow our example), you can use e.getClass().getConicalName():

try {
    Double x = 1 / 0; // ArithmeticException
}
catch (Exception e) {
    System.out.println(e.getClass().getConicalName()) // Will print "java.lang.ArithmeticException"
}