Simple programs, mainly for utility use, enjoy. Note: None of the following programs check for fuel nor go back and refill, this is because I play without fuel usage. Sorry about that.

Stair mine: Makes a 3x3 stair mine for the amount of layers you tell it. After it completes; it digs out the center to accomadate for not placing torches, to see lava before you go down, putting water at the bottom in the future to get down quick, ect.
Spoiler

pastebin get rEGbS5cN stair



x=0
print("How many layers down?")
layers=io.read()
layers=tonumber(layers)
layers=layers/2
for i=1,layers do
turtle.digDown()
turtle.down()
turtle.dig()
turtle.forward()
turtle.digUp()
turtle.digDown()
turtle.down()
turtle.turnRight()
turtle.dig()
turtle.forward()
turtle.digUp()
x=x+1
end
x=x*2
turtle.turnRight()
turtle.dig()
turtle.forward()
for i=1,x do
turtle.digUp()
turtle.up()
end
print("Finished!")

Platform Mine: It's probably the lowest quality program here. You need to type in length by width in the form of: 
plat l w
If you type in an odd number for width then it ends up on the other side, which I cannot fix for the life of me. If you do not type in the format stated previously, it wont return an error message. I think it'll explode and take your harddrive with it.
Spoiler

pastebin get QG5T5TiA plat



local tArgs = {...}
x=0
if tArgs ~=2 then
l=tonumber(tArgs[1])
w=tonumber(tArgs[2])
for i=1,w do
for i=1,l do
turtle.dig()
turtle.forward()
end
if x%2==0 then
turtle.turnRight()
turtle.dig()
turtle.forward()
turtle.turnRight()
elseif x%2==1 then
turtle.turnLeft()
turtle.dig()
turtle.forward()
turtle.turnLeft()
end
x=x+1
if x==w then
abort()
end
end
else
abort()
end

Bees: This is the most indepth one I've done as of yet (1/18/14). Put a turtle facing an apiary and a chest above (or change 'Up' on line 49 to 'Down' if you want to keep a chest below. Case matters.).
Then run the program with a princess and drone inside the turtle, any slot. The turtle will then ask for the lifespan of the bee. The times are spot on if you have constant day and never have rain. Otherwise they're pretty good estimates. It'll put the combs and whatever else doesn't go into the apiary into the chest after every switch.
Spoiler

pastebin get hqJUGwp0 bees



print("***Make sure bees are in the turtle")
print("before beginning***")
print("What is the life span of your bees?")
print("Shortest:1")
print("Shorter:2")
print("Short:3")
print("Shortened:4")
print("Normal:5")
print("Elongated:6")
print("Long:7")
print("Longer:8")
print("Longest:9")
x=io.read()
x=tonumber(x)
if x==1 then
time=285
elseif x==2 then
time=560
elseif x==3 then
time=835
elseif x==4 then
time=973
elseif x==5 then
time=1110
elseif x==6 then
time=1248
elseif x==7 then
time=1385
elseif x==8 then
time=1660
elseif x==9 then
time=1935
else
print("Ya' done goofed.")
abort()
end

while true do
for i = 1,9 do
turtle.suck()
end
for i=1,16 do
turtle.drop(64)
turtle.select(i)
end
print("Switched!")
for i=1,16 do
turtle.dropUp(64)
turtle.select(i)
end
sleep(time)
end

Bridge: Really basic bridge program, makes a 3-wide bridge until it hits solid land. It'll refill if it runs out of blocks in the selected slot. It'll tell you how many blocks it used and how many blocks it bridged. That really unnecescarily large block of code that could be replaced with a for i = loop was there when I was really awful at lua. Just learning, in fact. I keep it there as a reminder of how people are nice when you ask for help (nicely).

Spoiler

pastebin get WPF5nr3T bridge



local dis = 0
local pln = 0

function fill()
if turtle.getItemCount(1) == 0 then
turtle.select(2)
turtle.transferTo(1)
turtle.select(3)
turtle.transferTo(1)
turtle.select(4)
turtle.transferTo(1)
turtle.select(5)
turtle.transferTo(1)
turtle.select(6)
turtle.transferTo(1)
turtle.select(7)
turtle.transferTo(1)
turtle.select(8)
turtle.transferTo(1)
turtle.select(9)
turtle.transferTo(1)
turtle.select(10)
turtle.transferTo(1)
turtle.select(11)
turtle.transferTo(1)
turtle.select(12)
turtle.transferTo(1)
turtle.select(13)
turtle.transferTo(1)
turtle.select(14)
turtle.transferTo(1)
turtle.select(15)
turtle.transferTo(1)
turtle.select(16)
turtle.transferTo(1)
turtle.select(1)
end
end

turtle.forward()
while turtle.detectDown() == false do
turtle.down()
turtle.turnLeft()
turtle.place()
fill()
pln = pln + 1
turtle.turnRight()
turtle.turnRight()
turtle.place()
pln = pln + 1
fill()
turtle.up()
turtle.placeDown()
pln = pln + 1
fill()
turtle.turnLeft()
turtle.forward()
dis = dis + 1
print(pln.. "...")
end

print("Bridged ".. dis .." blocks, using "..pln.."blocks.")