A program that checks for Palindromness
notes:


Your coding style seems good. There is some inconsistent indentation,
but i am guessing that is a question formatting problem.
Having a static variable word means that palindrome is not 
threadsafe, and is confusing to call. either pass word to the
palindrome constructor, or make checkPalindrome() a static method
that takes a string.
checkPalindrome() outputs it's result to standard output. What if
you wanted to make your palindrome checker graphical?. have
checkPalindrome() return a boolean indicating whether word is a
palindrome or not. This concept of seperating model and output code
is extremly important.
Instead of wasting time and memory copy over the string backwards then
checking for equality, you can compare pairs of characters starting at
both ends of the string.
When you reverse the string, you can write a for loop that goes
backwards:

for (int i = word.length() - 1; i &gt;= 0; --i) {
    reversedChar = word.charAt(i);
    reversedWord.append(reversedChar);
}



example:

public boolean checkPalindrome(String word) {
    for (int i = 0; i &lt; word.length() / 2; ++i) {
        if (Character.toLowerCase(word.charAt(i)) !=
                Character.toLowerCase(word.charAt(word.length()-i-1))) {
            return false;
        }
        return true;
}