There are lots of Inline elements that you can use in place of Run, if you want an effect like underline, italics, or strike-through. However, if you want to apply an actual Effect, the element you are applying it to needs to derive from UIElement. Run and the other inline elements do not, but you can nest TextBlocks to be able to apply shader Effects like the DropShadow you are looking for.
<TextBlock>
<Run Text="This" />
<Italic>
<Run Text="has a" />
</Italic>
<TextBlock Text="Drop Shadow">
<TextBlock.Effect>
<DropShadowEffect />
</TextBlock.Effect>
</TextBlock>
</TextBlock>