2711 Concrete Slabs designed by Peter Eisenman accompany an entire city block near Brandenburger Tor.  The Designer has never provided an explanation of the monument instead allowing visitors to interpret the experience itself.  It's an incredibly powerful experience, especially if you visit the interpretive center below ground.

Taking 33 years, Hallgrimsur was designed to represent the lava flow of Iceland, particular the hexagonal rock formations of Svartifoss.  It's prominent placement in Reykjavik means it's easily located by tourists wanting to visit.

A pillar of Barcelona's identity, the church was started in 1882 and has never been completed making it the largest unfinished Catholic church in the world.  Gaudi spent 1883 to his death in 1926 working on the church, giving it a distinct look and architectural style, and at the time of his death, the church was only 25% complete.  Definitely worth a visit if you plan in incorporating Spain into your travels.  Frankly anything built by Gaudi is worth a visit!

Incredibly accessible from Dublin, Newgrange is a monument in a world of it's own.  A pre-historic monument from the Neolithic Age, Newgrange is dated to roughly 3200 BC.  It's fascinating to visit because scholars have never been able to agree on it's exact use, though do agree it has religious significance.  Access is by guided tour only and if you're lucky enough to win the Winter Solstice Lottery (roughly 20 names drawn each year), you will get to experience the phenomena of the architectural alignment to the Winter Solstice sun.  But if you don't win the lottery, every tour simulates the sun's behaviour during the 5 days of the solstice when natural light enters the mound.

Roughly 45,000 Canadians lost their lives during World War II, and according to the centre's website, 5500 of those souls were lost on the Beaches of Normandy.  The site is worth a consideration for every Canadian's European Bucket List if you're able.  Please visit Veterans Affairs Canada for more information about the Battle of Normandy and the role Canada played in WWII.

http://www.veterans.gc.ca/eng/remembrance/history/second-world-war/canada-and-the-second-world-war/normandy

Roughly a half hour train ride from Naples you'll find Pompeii.  During my first visit to Europe, with 8 countries under the belt, this was the monument that my friend found stuck out the most for her.  When Mount Vesuvius erupted in 79 AD, the city of Pompeii found itself covered in 4-6 of volcanic ash and pumice, desecrating the city and reducing the population to zero.  Pompeii remained lost for years, until the first discovery of it in 1599.  Since then there have been varying degrees of excavation.  For my friend and I, what we found amazing is that while we spent an entire day roaming the streets, we'd only a small fraction of the city that once was - work is still ongoing to excavate the city.  PLEASE, bring sensible footwear, water and if it's hot and sunny, consider taking an umbrella for shade.  While portions are doable if someone in your party uses a wheelchair, know that this is not a completely accessible site.

During World War II the Arrow Cross, fascist militia, executed roughly 20,000 Jews along the banks of the Danube in Budapest.  Lining people up, they were ordered to remove their shoes before being shot so their bodies would fall into the water.  The memorial was erected in 2005 and remains a poignant reminder of the Holocaust.

Numerous visits to Europe with numerous visits to a variety of monuments, memorials and sites and there is nothing I have experienced that compares to stepping foot inside any one of the concentration camps.  While there are many that one can go visit, Auschwitz was the largest center the Nazi's created, comprised of three camps and 45 sub-camps.  Estimates state about 1.3 million people set foot in Auschwitz, 1.1 million of whom died.  While Birkeanu remains a bit of an open air ground to walk around, Auschwitz I remains more of a museum, with multiple buildings and exhibitions to walk through and requires more time, in my opinion, than Birkeanu.  Guided Tours are available, but if you are more introspective and introverted like myself and my family, then doing the museum at your own pace with the use of a purchased printed guide might be the way to go. 

It's incredibly easy to find highlights in Germany to visit.  The country refuses to shy away from it's past instead highlighting it's own history for the world to see and learn from.  The Reichstag is no exception.  Access to the Reichstag is free, though you have to register for security clearance in advance.  You receive a headset to guide you through the history as well as the spectacular views from the dome.  From your vantage point you can see directly into the chamber, symbolizing the transparency of government, and that the people are who politicians work for.  It's an incredibly powerful example of symbolism, particularly against the background of the last 80-90 years.  While the inner dome is covered, it's neither water nor wind proof, so dressing for the weather is a must.

While the Coliseum is the obvious choice for a list like this, on my travels I found the charm of the Roman Forums even more appealing.  Both are doable in a half day, with the Forums directly next to the Coliseum.  For centuries, from as early as the 7th Century, this was the epicenter of Rome, Surrounded by ruins in the center of Rome's Metropolis, here you get a real taste of what the Roman Empire truly was.  To enhance your experience, I highly recommend that you visit with a guide.