Financial Type on Contributions - Receipt (on-line) template
In your question you state "We're not using Price Sets." In that case you must have multiple contribution pages, one for each financial type. 

You can edit the online contribution receipt to include something like:

{if $contributionPageId eq "4"}
     &lt;tr&gt;
     &lt;td colspan="2" {$valueStyle}&gt;
      {ts}Donation to General Fund{/ts}
     &lt;/td&gt; 
       &lt;/tr&gt;
{elseif $contributionPageId eq "3"}
     &lt;tr&gt;
     &lt;td colspan="2" {$valueStyle}&gt;
      {ts}Donation to Child Sponsorship Fund{/ts}
     &lt;/td&gt; 
       &lt;/tr&gt;
...


{/if}

I would place it in the receipt table just under the "Payment Details" header.

I realise it is a somewhat rudimentary solution, but "quick and dirty" is effective if you are struggling with tokens.