What is the English word for when you see something new, for example,
learn a new word, and that word or thing keeps popping up more
frequently?

illusion

fantasy  illusion  imagine  mirage

I don't know what the exactly meaning you want to express. the words
above i think have just give you a hint to think about.

This thread may be of interest:

http://www.answers.google.com/answers/threadview?id=402268

Perhaps some other words that will direct you is serndipity or coincidence

From the thread that Pink references, and still self-serving here, I go for
"sensitized" as the word you are seeking.  If you have been thinking about
"potato chips," you will start noticing newspaper and television ads for
potato chips, or people eating potato chips, as you are now sensitized (more
sensitive) to potato chips.

haunting

I'm not sure, but I believe something similar was discussed in
Gilovich's How We Know What Isn't So (very great and important book)
but I don't have it handy to see if there is a term for it.  It's some
kind of asymmetry.  Essentially, you are weighing the success of
hearing something you just learned far more heavily than you weigh the
failures.  You don't rememember all the times where you learn
something and *don't* hear about it soon after.  You also don't
remember all the times you heard the thing you just learned before you
learned it.

I think the example in the book has to do with the phone ringing while
 you are in the shower, and how it seems the damn phone always rings. 
But that is because you simply remember the times it does ring much
more vividly than the times it doesn't, even though the times it
doesn't ring far outnumbers the times it does.

If I can get my hands on the book I'll check. I think there was a term
he used for this phenomenon.

fascination  ??

deja-vu

I've notice this "phenomanon" may times before, I think it requires
exposure to may different things, i.e you read alot, you have many
interests, you are observant.

It's definitely not Deja-vu, that requires a perceived prior knowledge.

So I put my "vote" towards: coincidence.