[Old Pedant]

But you know, it would be better to keep the words paired, rather than depending on parallel arrays that could easily get out of sync. So:

<button onclick="nextWord(1)">Previous word</button>
<button onclick="showEnglish()">Answer</button>
<button onclick="nextWord(-1)">Next word</button>

<script type="text/javascript">
var words = [
    ["食べる",  "to eat"],
    ["読む",    "to read"],
    ["行く",     "to go"]
];
var wordCount = words.length;
var cnt=0;

function showEnglish()
{
    document.getElementById("english").innerHTML = words[cnt][1];
}
function nextWord( moveBy )
{
    cnt = ( cnt + wordCount + moveBy ) % wordCount;
    document.getElementById("japanese").innerHTML = words[cnt][0]
    document.getElementById("english").innerHTML='&nbsp;';
}
nextWord(0); // get it started
</script>