Girl Genius by Phil and Kaja Fogilo
Romance, adventure, mad science and talking cat emperors, welcome to the world of Girl Genius. Our heroine is Agatha Heterodyne, Spark and last known heir to house Heterodyne. Her adventure begins with Agatha under the assumed name of Agatha Clay and raised by her loving if mute, the comic can explain this a lot better than I can, step-parents Adam and Lilith Clay, blissfully unaware of her Heterodyne heritage and true nature as a Spark, basically an inborn mad scientist/engineer.
Agatha's adventures take her across the continent of Europa, evading the clutches of Baron Wolfgang Wulfenbach, the well intended if ruthless and morally ambiguous supreme ruler/tyrant of all Europa, amassing a small army of loyal and worshipful lackeys and gets entangled in a love triangle with the Baron's dashing if hotheaded son Gilgamesh and Tarvek Sturmvoraus, the charming and unfailingly polite if duplicitous prince and distaff descendant of the Storm King of old. Agatha does not find their fighting over her to be romantic, just aggravating. She even sets out to awaken Castle Heterodyne, hopefully without it killing her to show its affection.
The Adventures of Dr. McNinja by Christopher Hastings and Anthony Clark
First off, the main character is a doctor and a ninja, it only gets weirder from there. His receptionist and nurse is a female gorilla named Judy, who is capable of understanding multiple human languages, both spoken and written, but is incapable of speaking those languages. Which is due to the fact that she's a gorilla, with normal gorilla vocal cords, but she does know sign language. If only the good Dr. McNinja knew sign language too. Alas he doesn't, so they are forced to communicate with spoken English (on Dr. McNinja's part) and written responses. They manage pretty well.
Over the years the good Dr. McNinja has assembled a larger team around himself, including his own Bot Wonder, a 12 year old velociraptor riding gunslining bandito named Gordito Delgado. Together, Dr. McNinja, Gordito and his late father's gang of dinosaur riding banditos avenged the senior Delgado's murder. As a result young Gordito became the good doctor's sidekick and formed an especially close bond with Dr. MiNinja's pet velociraptor, Yoshi, now Gorditio's trusty and loyal steed. I feel like mentioning that Gordito's sheer will and determination to act like a real man and hunt down his father's murderer caused the 12 year old to grow a full, bushy mustache.
Over the years our hero has faced many deadly foes, from the unscrupulous clown and fast food mogul Donald McBonald over copyright infringement, to war against the corrupted German ninja Franz Rayner to end his program of artificially created ninja foot soldiers, clashing against Dracula within the Prince of Darkness's secret moonbase to his ongoing conflict with King Radical. But Dr. McNinja is more than just a fighter and often times killer. Like any good medical doctor he's also a healer.
It was none other Dr. McNinja who discovered the cure to Paul Bunyan Disease, a horrific disease that transforms children into 20 foot tall giants with jet black hair, full beards, flannel clothing and a berzerker's rage against all trees with desire to fell them all with their giant axes. The giant axes that just pop into existence along with the disease's other symptoms, including giant blue oxen to themselves. The disease's onset presents with the projectile vomiting of maple syrup. I've just about explained Dr. McNinja right now and it makes just as much sense in context. Oh, Dr. McNinja learned much of what he knows of medicine from Ben Franklin's clone. I'm officially done with this.
Atomic Robo by Brian Clevinger and Scott Wegener
The year was 1923 and Nikola Tesla was hard at work building a manlike creature of steel, glass and wires. It was like a son to him, Tesla's legacy and last great gift to the world. That was the day Atomic Robo was born. He battled Nazis and other enemies of humanity and world peace, as well as Doctor Dinosaur and other foes of intelligence and basic reasoning skills. His heroic career sees Atomic Robo fighting giant monsters, fellow robots, Doctor Dinosaur, rogue Soviet Generals and his long time adversary Thomas Alva Edison, who despises Robo for being a creation of Tesla's. In all, Atomic Robo is a two-fisted robotic pulp hero, with a list of friends and allies that include the hereditary British spies called the Sparrows, zen gunslinger Jack Tarot and the late astrophysicist Carl Sagan.
Kill Six Billion Demons by Abbadon (not the author's real name, I think)
This honestly is the webcomic in this post I know the least about. I get that it's about a normal young woman who finds herself in a magical world of gods, demons and angels and forced to fight to survive and explore the strange realm she's lost in. It features major battles involving sorcery, raw supernatural might and martial skill. Perfect inspiration for a high power campaign.