I do. my main character was a reseasch assistant that helped create the hospitals emergency teleportaion system and the medical regeneration tecnology. In fact she taps into the hospital teleportation system inorder to use her TP powers and miniturized copies of the regeneration system to heal.
Yeh I do my story of my scrapper is tied in with the story of the Rikti invasion
Absolutely! It's very common for players to intigrate their character history and background into the current events in the game.
Ivory denied the call to arms during world war 2 when every other hero around him accepted, something that pains him to this day as he makes special purchase twords fighting 5th column. The company that "employs" him makes great use of Crey biological properties and Ivory himself will claim to have developed the proprietary technology on which most of Portal Corporation's current developements are based.
Galactic Jack actively seeks the Rikti in hopes he can obtain technology adaquate to get him off the planet, allowing him to reclaim his "towed" spacecraft.
It's fun, almost everyone does it, it's very natural, first time is always free... want a sample? wait...
Actually while developing my main character I used the several of the CoH history to create her back story. Focusing on the Circle of Thorns primarily as well as the ailen envasion because of the world spanning nature of that event. Also, to flesh out the Order she belongs to I dipped into Persian Mythology and History to help create an original arch for her to play out. If you would like to read her background itÂ’s under The History of The Amesha Spentas and Armaiti. 
Most of my characters with backstories have them tied in to current events:
John Red Eagle (tech blaster, guns 'n' gadgets) - When he retired from Special Forces, he returned to the reservation and found that the Skulls had started to move in, recruiting and getting kids hooked on Superadine. John and his son Mike (a reservation police officer) drove them off but not before Mike was killed in a shootout. John vowed revenge against the Skulls. He gets help from "a few friends still in the Agency" and has moved to Paragon City to pursue his vengeance.
Umbrus (magic dark/dark defender) During the Rikti Invasion, the Circle of Thorns played a vital (if unacknowledged) role in defending Paragon City (as the aliens burrowed underground, they came to the CoT's secret city; the Circle defended it will all their resources and were likely instrumental in driving the Rikti off.) To supply hosts for the spirit beings that were at the source of the Circle's power -- and thus the Circle's defense -- hundreds of citizens were kidnapped and subjected to a horrifying rite that expelled their souls to the outer darkness, leaving living, empty shells. Terrence Conway was one of the people kidnapped. He was an adept of various dark arts himself and was able to return to the mortal plane. He is but a shadow of his former self, so he has taken the name of Umbrus (from Latin 'umbra', the darkness cast when a celestial body blocks out the sun.) His driving goal is to fight the evil that is the Circle of Thorns.
CD-4819 (tech rad/rad defender) A "civil defense unit" from about 2300 years in the future. According to his past, the Rikti Invasion was but a preliminary landing force. In 2048, the Rikti returned in even greater numbers. Their primary goal was to "mine" the Earth of its water and some rare heavy elements. The Earth became a waterless, almost airless world and all that remained of humanity was a "Morlock" class of Martian colonists and an "Eloi" class of space station dwellers. After two centuries of oppression, the Martians developped a type of bomb that altered the quantum nature of a small patch of space-time; they attacked the space stations and set off the bombs near the stations' reactors. As best as CD-4819 can tell, the result was a rift that sent him back to just after the first invasion. He has told the government to prepare, but is not sure if his warnings are being taken seriously or if they will do any good. He is working to develop his skills so that he is ready when the Rikti return.
Why yes... In fact, the Voidchild-stories here on the boards are actually loosely based on an assortment of missions she's been on... In fact, she even met Movian during one of them... ^^
Just wondering, does anyone else try to tie your backstory into whatever CoH mission/storyline you happen to be pursuing? For example, Gravotus has ties to the 5th column back from when some of their supporters relocated to South Africa during the Apartheid area and....
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I find doing this with other players familiar with my backstory vastly improves my RP experience in CoH so that I'm not whacking another group of Skulls or somesuch just cuz my contact said so (not a game criticism incidentally, I get jaded easily
Comments please.
-Gravotus, aka Stefan Gravotus