Mostrar texto en MouseOver para imagen en html

Puedes usar title atributo.

<img src="smiley.gif"  title="Smiley face"/>

You can change the source of image as you want.

Y como @Gris comentado:

También puedes utilizar la title on other things like <a ... anchors, <p>, <div>, <input>, etc. See: este

You can use CSS hover
Link to jsfiddle here: http://jsfiddle.net/ANKwQ/5/

HTML:

<a><img src='https://encrypted-tbn2.google.com/images?q=tbn:ANd9GcQB3a3aouZcIPEF0di4r9uK4c0r9FlFnCasg_P8ISk8tZytippZRQ'></a>
<div>text</div>
​

CSS:

div {
    display: none;
    border:1px solid #000;
    height:30px;
    width:290px;
    margin-left:10px;
}

a:hover + div {
    display: block;
}​

You can do like this also:

HTML:

<a><img src='https://encrypted-tbn2.google.com/images?q=tbn:ANd9GcQB3a3aouZcIPEF0di4r9uK4c0r9FlFnCasg_P8ISk8tZytippZRQ' onmouseover="somefunction();"></a>

En javascript:

function somefunction()
{
  //Do somethisg.
}

You can use CSS hover in combination with an image background.

CO

   .image
{
    background:url(images/back.png);
    height:100px;
    width:100px;
    display: block;
    float:left;
}

.image  a {
    display: none;
}

.image  a:hover {
    display: block;
}

HTML

<div class="image"><a href="#">Text you want on mouseover</a></div>