How can I remove the space between fields show in a view that are output with a custom template?
I just created a quick View here that had three fields:

1.  Node title.
2.  Node type.
3.  Global Custom Text Area


I changed the HTML Element and Wrapper HTML Elements to SPANs for the first two fields and also set them both to be excluded from display.

For the Global Custom Text Area, I rewrote its output to be [title][type] and got the titles smashed right up next to the node types without a space.

ADDITION:

You could also copy views-view-field.tpl.php to views-view-fields--smashed.tpl.php (or whatever your Views name is :) and then remove all the whitespace from there, eg, this template looks nice like this:

 &lt;?php something ?&gt;
   &lt;?php something else ?&gt;
   &lt;?php something else again ?&gt;
 &lt;?php yadda yadda ?&gt;


and each of those lines and indents puts in the whitespace that is causing your grief.

If instead this is saved as

 &lt;?php something ?&gt;&lt;?php something else ?&gt;&lt;?php yadda yadda ?&gt;&lt;?php one really big long line of code without any intervening tabs or new lines or spaces ?&gt;


and your view will be created with the &lt;divs&gt; or &lt;spans&gt; smashed right up next to each other in the row.  Then CSS it up the way you want.