'i' and 'a' (mnemonic: the 'a' grabs all of something (and its white space) as opposed to 'i' which grabs the inner part) as modifiers for 'c', 'd', 'y', and 'v' can be very useful, but I don't see them talked about much in most tutorials.

See :help motion.txt - they're in section 6. Text Object Selection. Also, just play around with them a little. For example:

   <p>This is a tes|t. Do not be alarmed.</p>

If that's your text, and the cursor is at the pipe:

    ciw  # remove all of 'test', enter insert mode
    caw  # remove the word 'test' and preceding space, enter insert mode
    vit  # visually select all the text within the <p> tags
    vat  # visually select the whole <p> element

Check out this: http://blog.interlinked.org/tutorials/vim_tutorial.html (text-objects section in particular).

You can use other characters too: like ', {, [, (, t (HTML tag).

Even better, you can use b instead of ( and B instead of {, because it's easier to type.

same here, though i quite religiously use df" and d%.