How much lift would I need to put on my F-150 in order to fit 44" tires under it?  

You need more than lift. You need new axles and gears too. 44's are getting into rockwell territory if you want it to be as tuff/strong as it looks.  

Like the old saying goes, if you have to ask, you probably don't wanna know. If you're intent on keeping all your sheetmetal, you are probably looking at a 12-inch lift (minimum) for this. Problem is, most of the bigger (10- to 12-inch) lift kits you'll find on the market nowadays for Ford trucks are for the bigger late-model versions---Super Dutys, Excursions, etc. For the half-ton, you are probably looking at a 4- to 8-inch lift as that's what most of the manufacturers have for sale nowadays---which means you will either need to lose some sheetmetal or use some combination of extended shackles, spacers and/or blocks (which I don't recommend, ever) along with whatever lift kit you can find for your truck.

(I'm assuming your truck is a 1980-or-later model. If not, it's gonna be a lot harder to find off-the-shelf aftermarket parts for it.)

Besides stronger axles and a new set of ring-and-pinions mentioned earlier, you are also looking at plunking down for a set of thicker-wall driveshafts with heavier-duty U-joints and yokes. You will also need to modify (i.e., swap out) your steering linkage to compensate for the change in geometry that accompanies the lift, and those heavier tires and wheels are gonna require much bigger brakes too. All that extra weight is gonna put a strain on your stock engine and tranny, so you will probably want to consider installing some power hop-ups---air intake and manifold, headers, freer-flowing exhaust, etc. This in turn will place a strain on your stock cooling system, so you may want to consider upgrading your radiator and converting to an electric fan, as well as installing aftermarket tranny and engine oil coolers. Had enough yet?

This isn't meant to discourage you from going for the lift and 44s. Plenty of guys have done it---it just takes a fair amount of planning and preparation, some spare time, and plenty of disposable cash to Do It Right, keeping in mind how one modification to your truck can affect a whole slew of other components.  

Actually for what it is worth if you take the time to proper gear the axles you use for tire size in use there is not need for bigger drive shaft and joints. This whole drive shaft unjoint need is born out of end user that are too lazy or cheap to regear and the result is reduced performance and very high drive shaft loading. If you gear axles properly, you will not have any problems with stock drive shafts or joints in them. (other than maybe ujoint angle issues that require a custom CV)  

Well so far I have worked out on paper an ok set up for a 393 stroker which will produce about 450-500 horse and 500-550 torque that I am going to drop in.  I have also talked to a guy at a shop who had suggested running 5.33:1 gears, 35-spline 8-lug axles, posi, all the beefed up drive shaft and components.  The back brakes are drum which I will have converted over to disk and have both sets of brakes beefed up to, and deffanatly a beefier powersteering pump.  He also suggested that if I wanted, for extra beefyness, he could weld up a brace on the back of each axle tube to keep it from twisting.  He is used to working on mostly drag cars but he has done a rig or two hear and there.  I have looked at fourwheelparts.com and all of the lift kits they had for my truck ('76 F-150) went to 9" max.  I guess I am just wondering what kind of clearance I would need for not only the tires themselves but to allow for suspension travel.  I dont mind cutting some sheet metal if I have to.  The truck used to be a farm truck and the paint job is going to be a cheepo rattle can job anyway.  The truck is going to be used for mud bogging only, if it climes a dirt hill or two that would be it.  Also what do you think would be a good brand of lift kit to look for?  That is...if they do have anything for my truck (hopefully).  Thanks for all the input, deffanatly appreciated.  

For what it is worth, you are not going to get 500 ft lbs out of a 393 or even close to it let along 550 without a super charger or forced induction and if you cam it high enough to make over 400 HP it is going to be pretty gutless at lower RPM's. When you build and cam a engine for a heavy SUV focus on midrange power. Engines built to make best torque at middle to lower RPM also tend to have higher peak torque values too.