Not Blood Siblings — Liechtenstein and Switzerland. Of course, this also means that there's nothing really standing in the way of the obvious Ship Tease and tension between the two.
There's also the subtext of their relationship being so close as to be borderline incestuous.
Rags to Riches — Both of them. On one hand Liech was this close to dying when her lands went bankrupt due to war and the Great Depression, until Swiss took her in. On the other hand, Switzerland's own economic situation was very precarious when he found and adopted Liechtenstein, for exactly the same reason. Now both countries are extremely rich, with Liechstenstein as one of the richest nations in the whole world.
Yodel Land — Kiku/Japan is ruthlessly and hilariously disabused of his Heidi-style notions by meeting Vash. Liechtenstein and her blond pigtails and lacy skirts arguably play it straight though.
Morality Pet: Who knows how much more of a jerk he would be without Liechtenstein around.
Real Men Wear Pink: Girly pink pyjamas, that is. They're a present from Liechtenstein; she gave him the wrong ones by mistake, but he doesn't mind... because they're from his sister.
The Gunslinger: His Weapons Of Choice are several different guns, but personality-wise, he's more like a parody of the trope. Not to be confused with that otherVash, though.
Trademark Favorite Food: Cheese. Not too susprisingly that Switz people eat most cheese in the world.
Fan Nickname: She doesn't have an official human name, but some fans call her "Lili Zwingli" to bypass that. It comes from a shortening of her nation name and from the Lily flower, which is sometimes considered to be a national flower of Liechtenstein.
Himaruya himself in a recent blog post suggested her likely human name to be Erica/Erika, Sisia, Elise, or Eva, with her possible surname Vogel.
Heartwarming Orphan: According to the published manga, the poor little girl was on her own and passed throughseveral hardships before she was found and adopted by Switzerland. No mention of her "biological" parents or anybody who took care of her and her people until then.
This could also add some Alternative Character Interpretation when one considers her relationship with (and possible abandonment by) Austria and Hungary up until then.
Important Haircut: Liechtenstein used to have long braids. At the beginning of her first strip, she cuts said braids off to both look more like her brother and be more comfortable. The webcast episode featuring these strips actually begins with her cutting off said braids.
The Gunslinger: In Fanon as a consequence of her emulating Switzerland constantly. She has been occasionally shown in some sort of military training with him, carrying a rifle on her back, so somewhat confirmed.
The Unpronounceable: At one point in the dub, the Narrator apparently has trouble pronouncing Liechtenstein's name correctly. When she does, the child audience cheers.
What Could Have Been: At first Himaruya considered having her emulate her brother even more, with a harsher personality and a cold manner of speech.