How to set a stroke-width:1 on only certain sides of SVG shapes?

Setting a stroke-width: 1 on a <rect> element in SVG places a stroke on every side of the rectangle.

How does one place a stroke width on only three sides of an SVG rectangle?

If you need stroke or no-stroke then you can also use stroke-dasharray to do this, by making the dashes and gaps match up with the sides of the rectangle.

rect { fill: none; stroke: black; }
.top { stroke-dasharray: 0,50,150 }
.left { stroke-dasharray: 150,50 }
.bottom { stroke-dasharray: 100,50 }
.right { stroke-dasharray: 50,50,100 }

<svg height="300">
    <rect x="0.5" y="0.5" width="50" height="50" class="top"/>
    <rect x="0.5" y="60.5" width="50" height="50" class="left"/>
    <rect x="0.5" y="120.5" width="50" height="50" class="bottom"/>
    <rect x="0.5" y="180.5" width="50" height="50" class="right"/>
</svg>

See jsfiddle.

You cannot change the visual style of various parts of a single shape in SVG (absence the not-yet-available Vector Effects module). Instead, you will need to create separate shapes for each stroke or other visual style that you want to vary.

Specifically for this case, instead of using a <rect> or <polygon> element you can create a <path> or <polyline> that only covers three sides of the rectangle:

<!-- Move to 50,50 then draw a line to 150,50, to 150,150, and then to 50,150 -->
<path d="M50,50 L150,50 150,150 50,150" />
<polyline points="50,50 150,50 150,150 50,150" />

You can see the effect of these in action here: http://jsfiddle.net/b5FrF/3/

For more information, read about the <polyline> and more-powerful-but-more-confusing <path> shapes.