Try to use the following code in the template where the $subcategories array is defined:
Code:
{assign var="cell_counter" value="0"}
{assign var="subcat_per_row" value="3"}
<table width="100%" cellspacing="5">
{foreach from=$subcategories item=subcat}
{math equation="x+1" x=$cell_counter assign="cell_counter"}
{if $cell_counter eq "1"}<tr>{/if}
<td><a href="home.php?cat={$subcat.categoryid}"><img src="{$subcat.categoryid|func_get_image_url:C|default:"image.php?id=`$subcat.categoryid`&type=C"}" alt="{$subcat.category|escape}" style="padding-right: 5px;" align="left"/>{$subcat.category}</a></td>
{if $cell_counter eq $subcat_per_row}
</tr>
{assign var="cell_counter" value="0"}
{/if}
{/foreach}
{if $cell_counter gt 0}
{section loop=$subcat_per_row name=cc start=$cell_counter}
<td> </td>
{/section}
</tr>
{/if}
</table>
Also, I'd recommend you to move your category images to the file system. You can perform it under admin area on the "Images location" page.