What is the term for taking photos and videos of people with your
phone, and posting it on the internet?

For example, having an online 'diary' on the internet has been coined 'blogging'.

So if I used this term on a search engine, I would be directed to
numerous bulletin boards where people post the random pictures and
videos they have taken with their phones.

Greetings burnt_toast!

The term you are looking for is "moblog" - which is a word created
from the combination of mobile and weblog.  The general meaning is "A
mobile weblog, or moblog, consists of content posted to the Internet
from a mobile or portable device, such as a cellular phone or PDA."

above quote from "Moblog entry at Wikipedia":
http://en.wikipedia.org/wiki/Moblog

The following site has many links to people who moblog:
http://www.moblogging.org/

One popular site is TextAmerica:
"New Camera Phone Images at Textamerica.com":
http://www.textamerica.com/moblogs.aspx

When searching on Google, you will want to search not only on "moblog"
but also "moblogging" and "moblogs"

I hope the information above is helpful.  If you would like me to
further clarify or research the question, please let me know before
issuing a rating.  Thanks!

leep-ga

awesome!