Ew.
Okay, Owen, I'll never have the chance to confront you concerning this issue, but even so, please don't give me some "she has a good personality" crap.

One word.  Ew.
THOSE WHO ARE FAINT OF HEART, DO NOT SCROLL DOWN!
I've taken the liberty to zoom in on this picture for you.  Just look.  This lady is falling apart, not to mention flat out nasty.
 
Owen is a fine lookin' man, and Sheryl Crow is a pushin' 50 wannabe surfer/stoner songwriter whose croons are at best somewhat amusing (and granted, annoyingly brain searing.  My favorite of her songs is the "I don't have digital, I don't have diddly squat-" line from "Soak up the Sun."  It shows her tremendous lyrical power.  Me?  Sarcastic?  Nooooo.) 

Okay, I'm sorry.  Famous people have feelings, too.  Ahem.  "She has a wonderful personality."
Please tell me Owen was high or drunk when he made this poor relationship decision.
Man-ish
shoulders
It's really sad that a millionaire can't have someone do her makeup and hair better than this.
^ This nastiness of a shirt would definately make the Glamour "Don't" page
Why does her stomach protrude farther than her boobs?
<<<<
To be fair, I must mention the magic makeover she has recently gone through, for all of you Sheryl fans.  I've included a picture of her where she looks really good for affirmative action or something like that.
See, it just goes to show.  Sheryl, it pays to have professional hair and makeup done (not to mention plucked eyebrows) and a person good at photo touchups on staff. 
Sheryl Crow does look great here.  But dang girl, you need to have these pics pasted on your head cuz you look torn up most of the time.
Notice that this is way before Sheryl had her little makeover (shown above.)  She was pretty much in major need of a comeback look and record here.  Three clips on that mop of hair, and you would have a mullet.  You know it was time for a change.
EW
Owie ain't lookin' so hot in his pic either, though.
I'll never understand that little moment of insanity on Owen's part.  Was it for the fame?  The sex?  The mullet?  The "good personality"?  Frankly, it's not that deep for me. 

So we are moving on now.
It's perhaps important to note that Sheryl and Owen began dating at the height of her popularity, and the beginning of his.  Perhaps he was dazzled by her fame (as some would be of his fame now)?  It's sad, but probably a lot of couples in Hollywood hook up that way.