A couple of years ago ABC had a pilot show that ran for maybe 3
episodes before being canceled. From what I remember it was a popular
show in the UK. I remember the first show being about a young women
living in the city, NYC maybe?, and her events in and near her
apartment, but the main thing I remember is the theme song for the
show was "Touch & Go - Would You...?" If anyone could tell me the
American show name or the UK version, that'd be Great.

I believe you're remembering "As If," a show that began in the UK and
"crossed the pond" in 2002. The American remake, also called "As If,"
was a flop, and it was canceled after only two episodes had aired. The
show featured six characters: Sooz, Alex, Rob, Jamie, Sasha, and
Nikki. Each episode was shot from the point of view of one of the
characters. The theme song was, as you've recalled, Touch & Go's
"Would You...?"

Here are the names of the cast:

Internet Movie Database: "As If" (2002) [TV-Series]
http://imdb.com/title/tt0313034/

You'll find a photo and a brief description here:

Yahoo! TV: As If
http://tv.yahoo.com/tvpdb?d=tvi&cf=0&id=1807778485

Here's the show's listing from TV.com:

"As If (US)...
Tuesday 9:00 PM on UPN (30 mins) 
Status: Ended 
Premiered March 5, 2002 
Show Category: Comedy , Drama 
As If (US Version) was a teen drama series set in Los Angeles,
focusing on six friends, often with an entire episode shot from one of
their perspectives. This was a unique show due the cameras techniques
and the well written scripts, also it presented modern topics that
were common among teen in this era. Unfortunately the US version
didn`t have as much success as the English version, and only seven
episodes were produced. Only two were aired."

TV.com: As If (US)
http://www.tv.com/as-if-us/show/7448/summary.html&full_summary=1

I hope this is helpful! If anything is unclear or incomplete, or if
this is not the show you were thinking of, please request
clarification; I'll be glad to offer further assistance before you
rate my answer.

Best regards,
pinkfreud

Wow. That's it! 
Awesome job, that's way more then I could have expected.
Thank you so much.

Thank you very much for the five stars, the kind words, and the generous tip!

~pinkfreud