What do you want to remove..."My Account" or the complete "Account" menu ?
Removing the complete menu can be done with 'removeblock' like:
<reference name="the.parent.name.where.the.block.is.nested.in">
<remove name="name.in.layout.not.blockclassname"/>
</reference>
Best to do this in your own layout.xml file.
Or if you want to remove just one link, like this one:
<default>
<!-- Mage_Customer -->
<reference name="top.links">
<action method="addLink" translate="label title" module="customer">
<label>My Account</label>
<url helper="customer/getAccountUrl"/>
<title>My Account</title>
<prepare/>
<urlParams/>
<position>10</position>
</action>
</reference>
</default>
But you have to understand the fall back pattern of Magento. I'm using a theme called RDW now. So i have to change this to customize the RDW theme. So, if RDW has this in one of his xml layout files, changing the underlaying theme file 'base/default' for example doesn't work. Because it will use the RDW folder, assuming you didn't create your own fall-back order.
If you put this just as an example in:
{app/design/frontend/{package}/{theme}/layout/customer.xml}
<default>
<reference name="top.links">
<!-- line 162: Mage_Page_Block_Template_Links -->
<action method="removeLinkByUrl">
<!-- line 312: Mage_Customer_Helper_Data -->
<url helper="customer/getAccountUrl"/>
</action>
</reference>
</default>
The link will be removed, but it's a bad practis to change core files. So you create your own layout xml file and register it in a config.xml or better, create your own 'theme' on top of the previous one. So, it's easier to undo it.
But you have to re-ask a DESIGNER... or read the (designer) manual.
Good luck and happy hacking....
(Ps: Don't forget to flush layout & block cache. And never CHANGE MAGENTO CORE FILES. Doesn't matter if the sollution works. If you don't know always read the manual. Most awnsers on the internet including this forum can bite you in the future :-)
System > Configuration > Developer
to see in what file the link is outputted. Also, are you using a custom or purchased template?