Can I catch multiple Java exceptions in the same catch clause?

This has been possible since Java 7. The syntax for a multi-catch block is:

try { 
  ...
} catch (IllegalArgumentException | SecurityException | IllegalAccessException |
            NoSuchFieldException e) { 
  someCode();
}

Remember, though, that if all the exceptions belong to the same class hierarchy, you can simply catch that base exception type.

Also note that you cannot catch both ExceptionA and ExceptionB in the same block if ExceptionB is inherited, either directly or indirectly, from ExceptionA. The compiler will complain:

Alternatives in a multi-catch statement cannot be related by subclassing
  Alternative ExceptionB is a subclass of alternative ExceptionA

The fix for this is to only include the ancestor exception in the exception list, as it will also catch exceptions of the descendant type.

Not exactly before Java 7 but, I would do something like this:

Java 6 and before

try {
  //.....
} catch (Exception exc) {
  if (exc instanceof IllegalArgumentException || exc instanceof SecurityException || 
     exc instanceof IllegalAccessException || exc instanceof NoSuchFieldException ) {

     someCode();

  } else if (exc instanceof RuntimeException) {
     throw (RuntimeException) exc;     

  } else {
    throw new RuntimeException(exc);
  }

}

Java 7

try {
  //.....
} catch ( IllegalArgumentException | SecurityException |
         IllegalAccessException |NoSuchFieldException exc) {
  someCode();
}

Within Java 7 you can define multiple catch clauses like:

catch (IllegalArgumentException | SecurityException e)
{
    ...
}

No, one per customer prior to Java 7.

You can catch a superclass, like java.lang.Exception, as long as you take the same action in all cases.

try {
    // some code
} catch(Exception e) { //All exceptions are caught here as all are inheriting java.lang.Exception
    e.printStackTrace();
}

But that might not be the best practice. You should only catch an exception when you have a strategy for actually handling it - and logging and rethrowing is not "handling it". If you don't have a corrective action, better to add it to the method signature and let it bubble up to someone that can handle the situation.

With JDK 7 and later you can do this:

try {
    ...     
} catch (IllegalArgumentException | SecurityException | IllegalAccessException | NoSuchFieldException e) {
    someCode();
}

If there is a hierarchy of exceptions you can use the base class to catch all subclasses of exceptions. In the degenerate case you can catch all Java exceptions with:

try {
   ...
} catch (Exception e) {
   someCode();
}

In a more common case if RepositoryException is the the base class and PathNotFoundException is a derived class then:

try {
   ...
} catch (RepositoryException re) {
   someCode();
} catch (Exception e) {
   someCode();
}

The above code will catch RepositoryException and PathNotFoundException for one kind of exception handling and all other exceptions are lumped together. Since Java 7, as per @OscarRyz's answer above:

try { 
  ...
} catch( IOException | SQLException ex ) { 
  ...
}

A cleaner (but less verbose, and perhaps not as preferred) alternative to user454322's answer on Java 6 (i.e., Android) would be to catch all Exceptions and re-throw RuntimeExceptions. This wouldn't work if you're planning on catching other types of exceptions further up the stack (unless you also re-throw them), but will effectively catch all checked exceptions.

For instance:

try {
    // CODE THAT THROWS EXCEPTION
} catch (Exception e) {
    if (e instanceof RuntimeException) {
        // this exception was not expected, so re-throw it
        throw e;
    } else {
        // YOUR CODE FOR ALL CHECKED EXCEPTIONS
    } 
}

That being said, for verbosity, it might be best to set a boolean or some other variable and based on that execute some code after the try-catch block.

In pre-7 how about:

  Boolean   caught = true;
  Exception e;
  try {
     ...
     caught = false;
  } catch (TransformerException te) {
     e = te;
  } catch (SocketException se) {
     e = se;
  } catch (IOException ie) {
     e = ie;
  }
  if (caught) {
     someCode(); // You can reference Exception e here.
  }

It is very simple:

try { 
  // Your code here.
} catch (IllegalArgumentException | SecurityException | IllegalAccessException |
            NoSuchFieldException e) { 
  // Handle exception here.
}

For kotlin, it's not possible for now but they've considered to add it: Source
But for now, just a little trick:

try {
    // code
} catch(ex:Exception) {
    when(ex) {
        is SomeException,
        is AnotherException -> {
            // handle
        }
        else -> throw ex
    }
}

Catch the exception that happens to be a parent class in the exception hierarchy. This is of course, bad practice. In your case, the common parent exception happens to be the Exception class, and catching any exception that is an instance of Exception, is indeed bad practice - exceptions like NullPointerException are usually programming errors and should usually be resolved by checking for null values.