[gizmo]

You can turn it off in products list only:
General Settings > Appearance Options > Displaying Products

To remove it from visual view (Product Details) but keeping it within your template from Product Details in case you want it back again:

Go to:
Skin1/Customer/Main/Product_details.tpl

Look for:

<tr>
<td class="property-name">{$lng.lbl_sku}</td>
<td class="property-value" id="product_code" colspan="2">{$product.productcode|escape}</td>
</tr>

Replace with or add what I have highlighted in red, this will completely remove it and the Table from details, to switch it back on just remove the highlighted red....

{*<tr>
<td class="property-name">{$lng.lbl_sku}</td>
<td class="property-value" id="product_code" colspan="2">{$product.productcode|escape}</td>
</tr>*}