Cardinals and ordinals, 1 to 100

Common Lisp, 88 82 80 bytes

(format t"~@(~{~R~^, ~}~).
~:*~@(~{~:R~^, ~}~)."(loop as i to 99 collect(1+ i)))

(It is part of the language, I hope you don't mind)

Output

One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, twenty-one, twenty-two, twenty-three, twenty-four, twenty-five, twenty-six, twenty-seven, twenty-eight, twenty-nine, thirty, thirty-one, thirty-two, thirty-three, thirty-four, thirty-five, thirty-six, thirty-seven, thirty-eight, thirty-nine, forty, forty-one, forty-two, forty-three, forty-four, forty-five, forty-six, forty-seven, forty-eight, forty-nine, fifty, fifty-one, fifty-two, fifty-three, fifty-four, fifty-five, fifty-six, fifty-seven, fifty-eight, fifty-nine, sixty, sixty-one, sixty-two, sixty-three, sixty-four, sixty-five, sixty-six, sixty-seven, sixty-eight, sixty-nine, seventy, seventy-one, seventy-two, seventy-three, seventy-four, seventy-five, seventy-six, seventy-seven, seventy-eight, seventy-nine, eighty, eighty-one, eighty-two, eighty-three, eighty-four, eighty-five, eighty-six, eighty-seven, eighty-eight, eighty-nine, ninety, ninety-one, ninety-two, ninety-three, ninety-four, ninety-five, ninety-six, ninety-seven, ninety-eight, ninety-nine, one hundred.
First, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth, thirteenth, fourteenth, fifteenth, sixteenth, seventeenth, eighteenth, nineteenth, twentieth, twenty-first, twenty-second, twenty-third, twenty-fourth, twenty-fifth, twenty-sixth, twenty-seventh, twenty-eighth, twenty-ninth, thirtieth, thirty-first, thirty-second, thirty-third, thirty-fourth, thirty-fifth, thirty-sixth, thirty-seventh, thirty-eighth, thirty-ninth, fortieth, forty-first, forty-second, forty-third, forty-fourth, forty-fifth, forty-sixth, forty-seventh, forty-eighth, forty-ninth, fiftieth, fifty-first, fifty-second, fifty-third, fifty-fourth, fifty-fifth, fifty-sixth, fifty-seventh, fifty-eighth, fifty-ninth, sixtieth, sixty-first, sixty-second, sixty-third, sixty-fourth, sixty-fifth, sixty-sixth, sixty-seventh, sixty-eighth, sixty-ninth, seventieth, seventy-first, seventy-second, seventy-third, seventy-fourth, seventy-fifth, seventy-sixth, seventy-seventh, seventy-eighth, seventy-ninth, eightieth, eighty-first, eighty-second, eighty-third, eighty-fourth, eighty-fifth, eighty-sixth, eighty-seventh, eighty-eighth, eighty-ninth, ninetieth, ninety-first, ninety-second, ninety-third, ninety-fourth, ninety-fifth, ninety-sixth, ninety-seventh, ninety-eighth, ninety-ninth, one hundredth.

Explanations

See Formatted Output to Character Streams.

• (format t "<control string>" <arguments>) formats the control string according to the (variadic) arguments and prints to standard output (because t)

• (loop ...) builds the list of integers from 1 to 100

• ~@( ... ~) capitalizes the string returned by the inner control string

• ~{ ... ~} iterates over the current argument and applies the inner formatting to each element

• Inside the iteration, everything that follows ~^ is not printed on the last iteration: this is used to add the comma-space separator between elements.

• ~R outputs current argument as a cardinal

• ~:R outputs current argument as an ordinal

• ~% outputs a new line

• ~:* reset the current argument to be processed as the previous one, which is used here to reuse the list of integers a second time.

Saved 2 bytes thanks to PrzemysławP.

Pyth, 366 342 340 bytes

Lcbdj=Y", "++rhJy"one two three four five six seven eight nine"3+tJ+y"ten eleven twelve"+=Nm+d"teen"=by"thir four fif six seven eigh nine"sm+dm++d\-kJKy"twenty thirty forty fifty sixty seventy eighty ninety"+=H"one hundred"\.jY+rh=J++y"first second third"m+d=T"th"tPby"ninth"3+++tJy"tenth eleventh twelfth"+m+dTNsm++Pd"ieth"m++d\-kJK+H"th."

Live demo.

342-byte version:

Lcbdj", "++rhJy"one two three four five six seven eight nine"3+tJ+y"ten eleven twelve"+=Nm+d"teen"=by"thir four fif six seven eigh nine"sm+dm++d\-kJKy"twenty thirty forty fifty sixty seventy eighty ninety"+=H"one hundred"\.j", "+rh=J++y"first second third"m+d"th"tPby"ninth"3+++tJy"tenth eleventh twelfth"+m+d"th"Nsm++Pd"ieth"m++d\-kJK+H"th."

366-byte version:

Lcbd
j", "++"One"+tJy"one two three four five six seven eight nine"+y"ten eleven twelve"+=Nm+d"teen"y"thir four fif six seven eigh nine"sm+dm++d\-kJKy"twenty thirty forty fifty sixty seventy eighty ninety"+=H"one hundred"\.
j", "+"First"+++t=Jy"first second third fourth fifth sixth seventh eighth ninth"y"tenth eleventh twelfth"+m+d"th"Nsm++Pd"ieth"m++d\-kJK+H"th."

PHP - 491 bytes

Small cheat here for the cardinals (I'm using the NumberFormatter class that comes default with PHP):

echo'One, ';$x=new NumberFormatter(0,5);for($i=1;$i++<100;)echo$x->format($i).($i>99?
'.':', ');echo"
";$y=[First,second,third,fourth,fifth,sixth,seventh,eighth,ninth,tenth,
eleventh,twelfth,thirteenth,fourteenth,fifteenth,sixteenth,seventeenth,eighteenth,nineteenth,
twentieth];for($z=[thirtieth,fortieth,fiftieth,sixtieth,seventieth,eightieth,ninetieth];
$j++<99;$q=floor($j/10),$w=$z[$q-2])echo$j<21?$y[$j-1]:($j%10?$x->format($q*10).'-'.
strtolower($y[$j%10-1]):$w),', ';echo'one hundredth.';

(added a few new lines for readability)