OK, I suffer from insomnia often. usually because I get an idea bubbling around in my nearly empty head and can't let it go and just relax. Hey, an idea for me is a rare event, so I savor it as long as possible.

The latest one has been the classic "Time Travel Paradox" or, the usual, not well thought out dangers that can occur from traveling into the past and messing around with historic events.
The normal list of possible paradoxes are as long as the amount of sometime rather bright people that think them out. Puzzle Addicts with too much time on thier hands, or Writters who don't really care if thier concept is plausible or not, as long as it sounds cool.

So I was tearing into the whole concept, imagining this scenario and that one, thinking about the ramifications, Timeline effects, alterations to our current Reletive Viewpoint...Blah Blah Blah..
And getting more confused by the minute as my scenarios became more and more complicated and conveluted to make any sense. Most ended with a nearly infinit amount of alternate realities being born every frikken second or two if you ever DID manage to go back in Time..... Real headache stuff.

Then, in a galactic sized explosion, I had me an Epiphany! And it HURT! Ouch! (avoid them if you can!)
I was basing all my scenarios on other peoples ideas, things I had seen on TV or read in Books. few of these had any real science or serious thought put into them. most were ideas based on ideas based on rather slim assumptions or just fantasy.

With this embarassing and troubling realization in tow, I made a serious effort to clean my head of all the residue from decades of preconceptions and psuedo-facts and science and simply addressed the idea of Time Travel into the past, near or distant. The puzzle fell into clear understanding almost immediatley and with wonderful clarity.
Here is my theory and conclusions on Time Travel into the past, and all the resulting problems and paradoxes that can result. It might be handy to those who wish to write stories based on this theme.

1> Can we travel backwards in Time?

Answer> Sure, why not. Assuming the technology is eventually discovered.

The only REAL troubles you'll come accross is targeting a specific location to "Land" at. The Earth is only steady and stable beneath our feet from OUR relative viewpoint, standing on it. In reality, Terra is Spinning rather fast, and Orbiting Sol rather fast, and The whole Solar System is moving round our Galactic Center rather fast, and our Galaxy is moving through our Universe rather Fasest!..........
Now, try and figure out where the spot your standing right now was actually located 1000 years ago in Space? heck, figure it for 10 seconds ago if you want it easier. It was a LOOOOOONG ways away from where you are right now.
So the first dude to hop backwards in time through a cool ciclular-electromagnet-spinning-thingy-with-cool-FX will be sucking vacuum and lost to history as a huge OOPS!
A Time Machine will either move you through Space AND Time to a spot on Terra, or it will be a spaceship or starship or such. Maybe a Landing Pod that will be shot out at huge velocity towards the place in space that Terra was in 1million B.C. Then, as it creates a Time-Vortex or Worhole or such, it leaves real-space and accelerates outside einstienian space-time to near the spot you wanna land, re-entering normal space-time, decelerates to a landing right on top of a ticked off Tribal Witchdoctor, who has ruby slippers you can accessorize with!
It could HAPPEN!

2> Once back safely in the Past, Can I axe murder that Evil Dude from the past that I always thought the world would be better off without?

Answer> Did someone who looks exactly like YOU actually axe murder that dude according to history? then dissapear in a puff of logic? No?!?
Then there's your answer, you never did it Amigo! Nor did anyone else if it isn't recorded as being done.

So the answer to the favorite Paradox of all time is. You cannot go back in Time, and in a blaze of suicidal psychosis, Grease your own Ancestor. Because you DID NOT DO IT. The obvious evidense is that you EXIST. You cannot create a Paradox.

Alternate Timelines and Parallel worlds aside. There is not a chance you can ever go back and change a historic event. BUT! If history records that someone who looked alot like YOU was one of the Senators who butchered Julious Caesar in the Senate way back when. Then you likely were taking a Time-Vacation and got caught up in an historic event. Or you instigated the whole thing you evil bastard!
Remember, SOMEONE warned Caesar to watch his ass around the end of February (Kalends of February) or begining of March (Ides of March). This Oracle of things to come may very well have been someone trying to alter the timeline and see Rome become what it may have become had Caesar lived to accomplish his dreams.

It all falls beautifully into place once you realise the Past is not changeable. Time is a linear progression from then to here, if You DID do something to alter the past, it would be recorded as History well before you ever thought of doing the deed.
There are NO PARADOXES. period. End of debate.

BUT! this does not preclude, in any way, a Time Traveler being involved in historic events, or going back in unrecorded history (prehistoric or undocumented history) and having Loads of fun mucking things up for our ancestors. even recent history does not record everyone who ever had a philisophical chat with Stalin, or tried to talk Martin Luther King Jr. into a change of travel plans before his fateful speech. There is a HUGE amount of unknown or unmentioned area to play with for any Time-Travel Adventure. Even failed attempts at changing history are good fiction and wonderfully eventful.

As you see, sheddding the baggage of things you were programmed to think, and really thinking Outside the Box. Can really simplify your reality. Or clarify issues to the bare essense. But it is damn hard to do.