CJam, 50 49 bytes

Happiness and primality test

li_{Ab2f#:+}30*(T="happy""sad"?S@mp4*"non-prime">

Reads a number from STDIN. Both tests work only for 64-bit integers.

Try it online.

Own length

A"forTy-nine""l_{b2#:+}30*(=happsadS@mp4*pim>"?""

Prints forTy-nine.

Golfscript - 81

This program tests if a number is happy and/or prime.

~.:a;0.{).a\%!@+\}a*;2="""non-"if"prime"@ {`0\{48-.*+}/}9*("sad ""happy "if@@#get

This program, an anagram of the last, outputs "eighty-one" (its bytesize as a word).

;"eighty-one"#   !""""""""%()***++-..../002489:;=@@@@\\\`aaaaadffiimnppprs{{{}}}~

This should serve as an example.

CJam, 80 49 48 characters

UPDATE : Inspired by Dennis' implementation to calculate sum of squares of digits, here is a shorter version

Happy/Sad Prime/Non-prime:

ri:T{Ab2f#:+}G*X="happy""sad"?STmp4*"non-prime">

How it works:

ri:T                                "Read input as integer and store it in T"
    {       }G*                     "Run this code block 16 times"
     Ab                             "Convert the number into base 10"
       2f#                          "Calculate square of each digit"
          :+                        "Sum all the squared digits and put the sum on stack"
X=                                  "Compare the sum after 16th iteration to 1"
  "happy""sad"?                     "If sum is 1, put `happy` to stack, otherwise `sad`"
               ST                   "Put space on stack then put the value of T on stack"
                 mp4*               "Put 4 to stack if input is prime, otherwise 0"
                     "non-prime">   "Put `non-prime` to stack and slice out first four characters if the input number is prime"

forTy-eiGhT

""A"forTy-eiGhT""ri:{b2#:+}*X=appsadSmp4*nnpm>"?

How this works:

""                                  "Push empty string to stack"
  A                                 "Push 10 to stack"
   "forTy-eiGhT"                    "Push `forTy-eiGhT` to stack"
                "ri:....pm>"        "Push this string to stack too"
                            ?       "Keep `forTy-eiGhT` on stack and pop the other string"

Try it online

The first program reads the number from STDIN

My original 80 character solution

Happy/Sad Prime/Non-prime:

r:N{1/~]{i_*T+:T;}/T_s\1=:H!X):XK<&0:T;}g;H"happy""sad"?SNimp"prime"_"non-"\+?:Y

eigHTY

"eigHTY""r:N{1/~]{i_*T+:T}/_s\1=:H!X):XK<&0:T}happysad?SNmp";"prim_";"non-\?:+";