user850: This is always what gets me. I want to find a way to train myself to become more observant, and able to look at every piece that's about to murder me.

user70: This is a matter of discipline.  When it's your move, look at every one of your opponent's piece's moves. Look at every capture, look at every check.  There should never be a time when you're surprised by a one-move "peewee" shot.
This flows into a discussion on tactics, of which I am sure there are many questions already posed.
Anyway, when you're looking at captures and checks, be wary of moves that can pull your queen into the same line as your King, or pull a defending rook off the back rank.
If you post an example, we can give more concrete advice.

user672: As I mention here, not having any undefended piece greatly helps.

Each move, you have to check out for all your pieces, and after a few games of paying attention, it'll most probably become natural to know what pieces of yours are under somehow in peril, and not.
In case you missed some tactic, didn't count attacks and defenses well enough, whatnot, you always have at least one defender.
You'll start noticing overloads, which is probably a tactical trick beyond your level right now.

Eventually, you'll constantly have a map in your mind telling you :

this is attacked twice, defended by this and this : ✓
this is attacked once and defended by that : ✓
I can be put in check in various ways by his queen, but all my pieces are defended at least once : ✓
He just played this move, so this and that are threatened. I must find a move that defends both of them, e.g. moving one to defend the other, and I'll be fine.

Then, go look for problems that arise after multiple moves.

850: <p>This is always what gets me. I want to find a way to train myself to become more observant, and able to look at every piece that's about to murder me.</p>
 70: <p>This is a matter of discipline.  When it's your move, look at every one of your opponent's piece's moves. Look at every capture, look at every check.  There should never be a time when you're surprised by a one-move "peewee" shot.</p>

<p>This flows into a discussion on tactics, of which I am sure there are many questions already posed.</p>

<p>Anyway, when you're looking at captures and checks, be wary of moves that can pull your queen into the same line as your King, or pull a defending rook off the back rank.</p>

<p>If you post an example, we can give more concrete advice.</p>
 672: <p>As I mention <a href="https://chess.stackexchange.com/a/1610/672">here</a>, <strong>not having any undefended piece</strong> greatly helps.</p>

<ul>
<li><p>Each move, you have to check out for all your pieces, and after a few games of paying attention, it'll most probably become natural to know what pieces of yours are under somehow in peril, and not.</p></li>
<li><p>In case you missed some tactic, didn't count attacks and defenses well enough, whatnot, you always have at least one defender.</p></li>
<li><p>You'll start noticing overloads, which is probably a tactical trick beyond your level right now.</p></li>
</ul>

<p>Eventually, you'll <strong>constantly have a map in your mind</strong> telling you :</p>

<ul>
<li><p>this is attacked twice, defended by this and this : ✓</p></li>
<li><p>this is attacked once and defended by that : ✓</p></li>
<li><p>I can be put in check in various ways by his queen, but all my pieces are defended at least once : ✓</p></li>
<li><p><strong>He just played this move, so <em>this</em> and <em>that</em> are threatened.</strong> I must find a move that defends both of them, e.g. moving one to defend the other, and I'll be fine.</p></li>
</ul>

<p>Then, go look for problems that arise after multiple moves.</p>
