Prussia/Hungary
Childhood
Prussia and Hungary used to fight together when they were kids. Prussia was always ready for action and always easily wins in his battles. But Hungary easily beats him up when wanted to claim Burzenland. Prussia mentions in his diary what a creepy guy Hungary was.
Prussia thought Hungary was male. Hungary also thought that she was male as well, thinking that penises only grow when they become older.
War Days
When they did get older, Prussia became involved in wars against Austria, and enjoys beating the guy. Even if they're not in a battle, he still enjoys teasing and annoying Austria in any possible way he can. These things anger Hungary greatly, for she cares deeply for Austria, so she always beats Prussia up with a frying pan or simply with her fists, making Prussia severely injured and recollect no memory of what has happened to him. At times he also cries and begs for mercy when Hungary is about to torture him.
Modern Life
Although Prussia fears being beaten up by Hungary, he still attempts to do naughty things to her. In the Gakuen Hetalia game, he had been secretly peeping at the dressing room where Hungary changes her clothes.
Fan Speculations
Some fans speculate that Prussia has a crush on Hungary. There had been some hints that he had been jealous of Austria and Hungary's relationship.
Even though Prussia had successfully avoided marriages, he had been crying at the sight of Austria and Hungary together while claiming that he was just too happy being alone.
Though Hungary finds Prussia annoying, she doesn't want Prussia to die, saying that it'll be lonely without him.
WebManga Moments
[1] Liechtenstein’s Journal of Swiss Dopiness part 3
[2] Liechtenstein’s Journal of Swiss Dopiness part 4