Here's what I've found thus far :

I did not find any free apps to do this.

There are however numerous paid apps which can assist in this area.

An incomplete list of the applications I have found which do this, and a brief summary of my impressions follows.

1) AllYourTexts
http://www.allyourtexts.com/
$5.00 (15-day full trial)
very slick color-coded text output
graphical view of statistics of your text conversations
search capability through your conversations

doesn't handle emoji's, but includes pictures in its output

2) Copy Trans contacts
$9.99 (full capability trial, but limited to 50 transactions)
Very nice looking html output
doesn't handle emoji's, but does well with pictures

3) Decipher TextMessage
$19.95 (very crippled trial)
Nice looking html output.
Not sure how it handles pictures/emoji's (couldn't tell due to the crippled nature of the trial)

4) 3herosoft iphone SMS to Computer transfer
$14.98 -- meh

5) Backuptrans iphone SMS backup and restore
$19.95 (very crippled trial)
Text-based output that I'm not very impressed with, honestly
Doesn't handle pictures or emoji's well

6) Tansee iphone transfer
$19.95 (very crippled trial)
Text-based output that I'm not very impressed with, honestly
Doesn't handle pictures or emoji's well

I am currently using a two-pronged backup approach.

I really like the clean nice-looking color-coded text output and statistical capabilities of AllYourTexts.
I also like the very pretty html output of Copy Trans contacts.

I find it very interesting that the two programs I like best and fit my needs the best (seem most functional) are actually the two lowest-priced applications of all the ones I looked at.

Anyway I hope this helps you!!

Thanks!!

Any suggestions?

Thanks in advance!!!