If this tractor has a hydrostatic drive transmission.......and you were attempting to roll it manually (as in man-powered), this is not a defect.
Hydrostatic drive transmissions have a "free wheel mode" that must be enabled before you can roll them manually, even if you have the trans lever in Neutral. There is some type of lever or knob on the tractor that must be moved to the free position in order to roll manually.
So far as what you described about "one wheel rolls forward and the other backward" wheel raised off the ground.......that too is normal.
Check your owner's manual for complete details.
If you do not have your owner's manual, you can get one (maybe) by going to the Sears Direct website and plugging in the complete technical model number of your machine. Hint: LT1000 won't cut it, you must find the number on the tractor that begins with 917. or such. Will have 9 or more digits and might be on a decal under the seat.

good comments from mownie concerning hydrostatic drive.

here is another item to check. Most of these have a disc brake located on the transaxle. A lever is operated by the brake pedal to apply the brake. Sometimes the lever sticks due to wear, mis-adjustment or a buildup of grass.

This may be difficult to spot with the deck installed. With the deck removed, slide under the right side of the tractor and examine the brake linkage to the transaxle.
Wiggle the brake lever to make sure the brake is not applied.

Good words on the hyrdo.

Also, good words on the brakes. I have a newer LT1000 and had to clean out the brakes one time, though my problem was due to a lack of brakes.

Well, if the brake assembly gets full of dirt and/or gets rusty--you will probably not have brakes, unless the pedal gets stuck full "on".

Thanks for the info. I will definitely check out the brake assembly, as I have been able to manually roll the tractor in the past.

Yes, if the brake is froze up, the wheels would turn as you described when jacked up off the ground.

As mentioned above: Hydrostatic drive transmissions have a "free wheel mode" that must be enabled before you can roll them manually, even if you have the trans lever in Neutral. There is some type of lever or knob on the tractor that must be moved to the free position in order to roll manually.

I have an LT2000 and the level is located at the back of the tractor, up and to the right of where the hitch is. If the diagram there isn't warn off, it should tell you which way to lever should be...in or out.

Lots of good comments but in my case the mower works okay under power but with power off I cannot get it to roll forwards or backwards. The brake linkage looks okay. The freewheel lever pulls and locks. I can move the brake disc with my fingers.

massengale - dunno what machine you have (you don't say) - but try tracing back to other end of freewheel linkage - may be a sticking valve button, etc.

217275400 is the model number, an 06 model, 18hp 42inch, automatic. I plan to put it up on ramps and see what i can see without pulling the deck. i hate pulling the deck which i have done for every damn stump in texas

Today I was placing brake pads on Craftsman L T1 1000 put everything back together make sure everything was tightened up or a loose enough so everything when move now when I put it in gear the belt spends fine in the poli spends fine at normal speed but when it gets down to the axils on the transmission it barely spins

Did you remove a wheel and not get the wheel key back installed? Further help, post the chassis number from below the seat.

yeh the key was their but even when the tire is off the axil barly moves when in gear and the brake if off i did that to doble check to see if it was the break

I need help with my Lt 1000 as well the model number is 917 271920 not sure what year is it but my issue is that the axles won't spin when I put it in gear. It won't go forward or backwards it used to before I opened the transaxle to install the axle locks or whatever is called the ring that holds the axle in place and prevents it from sliding out. After I put everything back together it stopped working. There was this one washer that fell off when I first opened it and I had no idea where it belong and to be honest I do not know if I put it in the right place.