I do it every year.  

Won't hurt a thing, I do it to mine every year.  In some parts of the world burning off the remnants of last year's crop is just part of preparing for the next crop.  Depending on what gets burned it can help the PH of the soil, and may even put some nutrients back into the soil from the burned stalks, etc.

I used to until I started permaculture now that stuff is gold.

If you had any fungus (in major insect infestation) - burn is good (like vert wllt on your tomato plants), but the spores will be in the ground already as well.

Otherwise, if all the plants are healthy, compost them for a season if you have space.  I used to bury/till at the end of the season and that works reasonably well.   But some things like corn stalks have too much structure and take at least two seasons to break down.

I don't burning as you loose a lot more of the nutrients to the air.  And that nutrient breakdown in the ground also adds structure and food for microbes, earthworms, etc.  Ash doesn't return nearly as much.

But I do like a good bonfire!  

Remember, ashes are heavily alkaline. Tomatoes and some other veggies prefer acidic soil.

Maybe do a ph test yearly to make sure you arent messing with the balance of the soil.

I shred and fall plow my garden.  Then disk it smooth in the spring.  Dunno if it is "the best" but it is what I do.  

All fall and winter I pile all my leaves and branches and all sorts of yard stuff in my garden and burn it all and then till the ashes into the soil next spring.

In the past I had a neighbor who was burning some stuff in a not normal place to burn stuff.  This was in the country and we all had fire pits and what not, but he was off in a section of the field that was different.



I asked him what he was doing.  He said he was going to put a garden in that spot.  By getting a nice pile of stuff and burning it there the heat would kill off all the weed seeds in that area.



I have no clue if it works like that, but this fella knew a heck of a lot of interesting stuff and was fun to be around but his ups and downs could be a bit interesting.

I usually burn the weeds piled up in the garden. I also burn any veggie plants that were not healthy looking.
I do compost  leaves and cut grass for the garden. Also I hit Whole Foods for their brewed coffee grounds.