Spain declared neutrality during both WWI and WWII (though their position changed during WWII to nonbelligerent) though they did supply both sides during WWI and supplied the Axis powers and offered military support during WWII--it was a way to show that they sympathized with Germany et al. without formally entering the war. Being "neutral", though, some Spanish citizens went to join up and fight with the Axis, other volunteered to fight with the Allies. Spain is also more geographically removed from Europe, being separated from France by the Pyrenees--mountain ranges tend to be difficult to deal with when coordinating military movement and attacks.

The reason they didn't actively participate in the world wars really comes down to the fact that Spain had its own stuff going on. In the lead up to WWI, Spain entangled in the Spanish-American War (1898) over its colony, Cuba. They ended up losing several other colonies, too (Puerto Rico, the Philippines, Guam). They also really struggled to hold on to Morocco, getting entangled in some military action there just after WWI.

While the rest of Europe was taking a bit of a (uneasy) breather after WWI, Spain broke out into the Spanish Civil War (1936-1939) between the Nationalists and the Republicans. After such a brutal civil war, they really weren't ready or willing to be active participants in a much bigger conflict.

While it's true that Spain was neutral in both the world wars, the Spanish Civil War of the late 1930s almost certainly qualifies as "a major European war" and "event of the 20th century" - in fact, seeing an alignment of the future European Axis powers (Germany and Italy) on the side of the victorious Nationalists (led by Franco, whose ruled the country as a dictator for the following four decades). It was seen by many international observers as a front line in the war against European fascism.

I think its hard to understate the importance of the civil war in terms of cultural impact: it had a profound influence on George Orwell, Ernest Hemingway, Pablo Picasso, and W.H. Auden, among many others, and thousands of liberal/socialist/Communist foreigners served in international brigades on the Republican side.

Political historians of Spain will hopefully have a better answer as to the reasons for neutrality in both world wars; my understanding is that in both cases political gridlock made it difficult for the Spanish Republic (WWI) and Franco's government (WWII) to commit to either side.

Helen Graham's The Spanish Republic at War 1936-1939" (2002) is an excellent source on the Civil War itself.