I can't really name them in order, because they were all "favorites" at one point or another. There's no true spot for them on the list.
Rickey Henderson--- My first baseball card was a 1987 Topps of Rickey Henderson leading off of first base. Perhaps, because of this, he became my favorite player as a kid in my T-Ball/Minor League/Little League days.
Ken Griffey Jr.
--- The unofficial reason why I switched from the Oakland Athletics to the Seattle Mariners as my favorite team, aside from the fact that I lived within 100 miles of The Kingdome/Safeco Field most of my life.
Mark McGwire--- Roids or not, the guy was fun to watch. 500 ft. homeruns are awe-inspiring.
Ichiro Suzuki--- Still my favorite to win a HR derby, if he ever gets the shot. Once watched him put seven straight into the rightfield stands in batting practice - all line-drives. Fun player to watch.
Edgar Martinez--- Not sure I've seen anyone as skilled at taking a low and outside pitch down the right-field line. It was amazing to watch - and frustrating because I know I could never do that in 100 pitches.
Randy Johnson--- He threw bullets. As a kid, it was the one pitcher we joked that we'd never want to face in person. We somehow believed we could hit anyone except Randy Johnson.
Jamie Moyer--- Knuckleballers aside, has any other pitcher been so effective without a decent fastball? One coach once said if Jamie Moyer threw right handed, he'd be bagging groceries. Personally, I love watching him pitch - more accurately, I love watching the batters wave at his change-up in complete frustration.
Mickey Mantle--- If I could have the baseball talents of anyone in MLB history, it would be Mickey Mantle. In fact, he's generally the template I use for any created player I make in video games: switch-hitter with power and speed. Plus, he wore my favorite number.
Raul Ibanez--- I quickly became a fan when he first joined the Mariners. I liked his swing. When he came back I was very excited. He's also like Edgar - the guy has such a great swing to the opposite field. It's awesome.
--- What can I say? The question didn't restrict me to MLB players, so I have throw myself in there. While I haven't played anything outside of "Adult League Hardball" and slow-pitch since high school, I love playing and I love my "abilities" on the diamond: switch hitter, moderate speed, great glove with good range, injury free (knock on wood), and a true utility player (all positions, including P and C). And, as much as I love watching the other guys on this list play, I'd much rather be the player.