These examples are included in the manual and/or used for compiler testing.

From elsewhere:

hello.mad	 -- "Hello, world!" in MAD
beer.mad	 -- 99 Bottles of Beer
printcomment.mad -- test the PRINT COMMENT function
testmad.mad      -- Program that tests miscellaneous statements.
cubic.mad        -- cubic equation solver from the 1966 MAD manual.
dampsine.mad     -- Program to plot a damped sine curve.
printcomment     -- Program to test the PRINT COMMENT statement.
testfmt.mad      -- Program to test runtime format processing.
primes.mad       -- Program converted from FORTRAN by MADTRN to MAD.
testtape.mad     -- Program to test TAPE READ/WRITE BINARY terminate by count.
testtape2.mad    -- Program to test TAPE READ/WRITE BINARY terminate by EOF.

From the manual:

maxfunc.mad	-- implementation of n-argument max (I.6)
newton1.mad     -- roots of of a^x + x by Newton's method (I.9)
newton2.mad	-- roots of x^3 + ax^2 + bx + c by Newton's method (I.13)
invsf.mad	-- inversion function (II. 47)
quadratic.mad	-- roots of linear and quadratic equations (III.3)
truthtable.mad	-- print a truth-table (III. 6)
simpsfunc.mad	-- Simpson's Rule function (III. 8)
simpsmain.mad	-- Simpson's Rule main program (III. 9)
findroot.mad	-- find root by half-interval approximation (III. 13)
transfunc.mad	-- transpose function (III. 15)
matrixmult.mad	-- matrix multiplication (III. 17)
jordan.mad	-- simultaneous equations via Jordan elimination (III. 22)
payroll.mad	-- payroll-processing example (III. 27
altpayroll.mad	-- payroll-processing example in structured style (III. 28)
payrolltape.mad	-- payroll tape program (III. 35)
mortgage.mad	-- check mortgage payments (III. 40)
commutefunc.mad	-- actuarial commutation function (III. 45) 
commutemain.mad	-- driver for actuarial commutation function (III. 45) 
wordsearch.mad	-- search for a word in a string (III. 49)
factfunc.mad	-- recursive factorial implementation (III. 50)
factmain.mad	-- main program exercising factorial function (III. 51)
gcdfunc.mad	-- greatest common divisor function (III. 53)
gcdmain.mad	-- main program exercising GCD function (III. 55)
tschebfunc.mad	-- Tschebychev polynomial evaluation function (III. 57)
tschebmain.mad	-- main program exercising Tschebychev function  (III. 57)
