I am looking for a song written in the 80s, the mid 80s I think.  The
genre is pop/rock, or soft rock, and the artist sounds a bit like Mike
and the Mechanics.  I have some of the lyrics in my head, and here
they are:

-Taking in, taking in again, you said I'm the only one but we can be
just friends...
-And if you say....I don't believe it... And if you....I don't believe it...

That's "Taken In," sung by (you guessed it) Mike and the Mechanics!
It's from their first album, "Mike + the Mechanics," released in 1985.
The song was written by Mike Rutherford and Christopher Neil.

"Taken in, taken in again
 Wrapped around the finger of some fair-weather friend
 Caught up in the promises, left out in the end
 No pride, taken for a ride
 You say I'm the only one when I look in your eyes
 I want to believe you but you know how to lie

 And if you say you understand I don't believe it
 And when you reach out for my hand I don't believe it
 And if you say you take the blame I don't believe it
 And if say that nothing's changed I don't believe it, don't believe it..."

You'll find complete lyrics to "Taken In" here:

UpperCut Music: Mike and the Mechanics Lyrics - Taken In
http://www.uppercutmusic.com/artist_m/mike_and_the_mechanics_lyrics/taken_in_lyrics.html

You can listen to a brief audio clip here:

MusicNow: Taken In
http://www.musicnow.com/servlet/play?id=700352

Here's the CD (one of the best albums of the '80s, in my opinion):

Amazon: Mike + the Mechanics
http://www.amazon.com/Mike-%2B-Mechanics/dp/B000002IIG

My Google search strategy:

Google Web Search: "mike * the mechanics" "taken in"
://www.google.com/search?hl=en&q=%22mike+*+the+mechanics%22+%22taken+in%22

I hope this helps! If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud