Take some paper and make three columns down which you place the numbers 1 to 243.
Over the course of the day, write down the names of every country you can think of.
To give you a little help here are the breakdowns by letter:
A – 18
B – 18
C – 23
D – 4
E – 7
F – 6
G – 15
H – 4
I – 9
J – 4
K – 8
L – 9
M – 22
N – 16
O – 1
P – 13
Q – 1
R – 3
S – 30
T – 14
U – 7
V – 6
W – 2
X – none
Y – 1
Z – 2
Now, using a different color pen, take a look at a List of Countries and see how well you did. When you're done filling and correcting the names you missed, go read the entry for the first of the ones you didn't know.
If you do this every week, by the end of a year, you'll know about the whole world.
Discardia 
You should clarify that this list includes sovereign and non-sovereign states. There are actually only 194 sovereign states. For example, the list you linked to includes Puerto Rico, which is a “US overseas commonwealth”, not a sovereign nation.
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The Wikipedia link at the end has the full breakdown of the different categories. I was surprised by what a disconnect there is between “country” and “U.N. member” and “sovereign state”. Even without the fun of mentally going back through those childhood stamp collections, it’s a fascinating article.
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Just wanted to say thanks for this tip, you’ve really inspired me.
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You inspired me too. To think back to when my father and I used to play our little country-capital game. The rules are simple. One of you name a country and the other one has to name the capital. Great fun if you are a little map-crazy.
And thanks for some great advise/inspiration all through the year – I’ve been lurking since january…
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