Ascend to a Higher Plane of Existence: It's generally agreed "Schwarzer Sarg" is about death. Though depending on what translation you're looking at, it also tells a tale of a girl who died (possibly by suicide) and looks down and pities the rest of the human world. That, or it's just Word Salad Lyrics about death.
The band, and in particular, Yui, loves this trope. In addition to naming the band "Das Feenreich", many of their song titles and plenty of lyric lines are in German.
Just to drive the point home, they had an official live called 920Putsch.
Iconic Outfit: The one for Stigma qualifies to a lesser degree, but recently the hats from Gothic Lolita Doctrine and Pax Vesania have become very important. The Doctrine hat is generally worn during performances of "Patriot Anthem".
Ill Girl: The protagonist of "Kikai Shoujo Gensou."
Lighter and Softer: Their old indie albums, and the more recent "Irodori no Nai Sekai" and "Ashita wo Yurushite".
Mad Love: In "Filament". Considering it was used as one of the opening themes for Mirai Nikki it's most likely sung from Yuno Gasai's perspective.
Meaningful Name: "Hidden Truth" is a purely music box version of "Wahrheit". "Wahrheit" means "truth" in German.
Mondegreen: The chanting near the end of "Kikai Shoujo Gensou". Despite it being in Japanese, It's written in katakana in the lyrics book (which is the alphabet used almost exclusively for foreign words). Which makes translating quite difficult.
Mohs Scale of Rock and Metal Hardness: Whenever they dip into the realm of metal and hard rock, they can go as high as an 8 or a 7, as evident with "Kokou no Sousei", and arguably "Mischievous of Alice". Live versions of some songs tend to be considerably harder and louder.
Non-Appearing Title: Nearly all of their songs. A few exceptions are "Last Moment", "Kokou no Sousei", "Shito Raisan", and "Still Alive". "Call My Name" is a semi-example, as the English phrase appears nowhere in the lyrics, but its Japanese translation does.
Oh Crap: Basically the reaction of "Kikai Shoujo Gensou"'s protagonist as she realizes that getting this "perfect" machine body will take away her humanity.
Only Known by Their Nickname: Averted with Yui. Even though she officially goes by "Yui, Dictator for Life" in the band, she's also a voice actress, and it's pretty well known that her last name is Itsuki.
Robot Girl: What the aforementioned Ill Girl becomes.
Scare Chord: "Wisdom" starts out as a creepy little piano tune, then suddenly brings on the heavy guitars.
Soprano and Gravel: Yui frequently alternates between a cute, melodic singing voice to a creepy child voice in many of her songs with ease. Justified by the fact that she's both a singer and a voice actress.
Visual Kei: Many Visual Kei fans have classified them as one (or post-Visual Kei at the very least) ever since their Genre Shift into Heavy Metal, though they aren't as recognized as other female-fronted Visual bands such as Exist Trace and Danger Gang due to a slight negative stigma against "kawaii moe bishoujo" vocalists. Yui's costuming and image would certainly qualify, though. The two new members, Shiren and Gight, have pushed the band much further in this direction than before.
Zettai Ryouiki: Yui on the cover of Stigma. Has become a staple element of most of her outfits.