Not the subway…i saw tennis star Martina Navratilova in a Sports Authority and at A&P in my town. Didn’t talk to her, didn’t care
Saw Scottie Pippen at Old Orchard Theaters back when he was with Da Bulls.
Nop, nope, nope,. I’m sorry folks. The OP clearly stated that we’re looking for subway encounters. I’m afraid the rest of you are disqualified. But do try again in an upcoming contest. 
I made a sandwich for Larisa Oleynik from Nickelodeon’s Secret World of Alex Mack and Ten Things I hate About You. It sucked because at the time, I couldn’t remember her real name, and no one else knew who the hell I was talking about. Very anti-climactic, considering I had a crush on her for a few years. She said “Homina.” That was cool.
I once sat across from Lois Smith, the actress, on the uptown IRT local.
I shared an N Judah train with Debra Winger and her husband. Looking at other train passengers is usually a recipe for disaster so I almost never do so, but I recognized her voice. They got off at the same stop as me and went into the UCSF Medical Center. Nobody was paying any attention to them.
I saw Mike Dukakis (former Governor of Massachussetts and failed Presidential candidate) at the Longwood stop on Boston’s Green Line. He was famous for taking the subway to work as Governor.
By brother once chatted with Gene Shalit of the Today show on an Amtrak train on the Hudson River line.
Subway, shmubway…here in LA where there’s no real transit system to speak of, we must see our stars elsewhere!
I’ve seen John Lithgow several times walking his dogs early in the mornings on campus (his wife’s a professor here). I’ve seen Pete Sampras unloading stuff from his car. Hmm, oh yeah and Michelle Kwan was in my sorority house for dinner one time. One of her friend’s was a member. I saw Winnie (or however you spell it) from The Wonder Years at the movie theater.
And, I’ve been a watcher at the various premieres here in town so I’ve seen Tom Hanks and Rita Wilson and…Heath Ledger mmm I actually got to go see the premiere of A Knight’s Tale so when I was walking out with my friends I was standing RIGHT NEXT to Heath. Tall and sexy, just how I like 'em!
Oh, and one last one…this doesn’t really count either but I think it’s pretty darn cool…I went to a talent show put on my college and they were honoring Stevie Wonder. He and his brother sat 7 seats from me to watch the show and then when he accepted the award we all got an impromptu 20 minute concert…freaking cool! Even when he was on stage he was only like 15 feet away! wee!
Okay, I’m done going slightly off topic. Thank you for making me feel cool by association 
I’ve seen both Steve Buscemi and John Turturro on the F train (separately).
But Ron Jeremy…wow, now that’s a celebrity spotting worth bragging about.
[Hijack]Wife and I play a agame where, if we see someone who looks vaguely like a celebrity, we “spot” them (e.g., see a guy who looks vaguely like Paul Newman and say “Paul Newman”). I am pretty poor at this game, so much so that one day I saw a guy who looked like Henry Rollins on Houston Street and went “Henry Rollins”…and it was actually him.[/Hijack]
The title says subway, so I’m sticking with subway. Headed on the (mumble) train downtown from Lincoln Center, I ran into Anthony Heald. He plays weasely guys, in particular the weasely Dr. Chilton from Silence of the Lambs. He was in the play Anything Goes at the time, and I’d seen it the day before, so I got his autograph. Seemed really friendly, and not at all weasely.
I sat across from Canadian actress Julie Kahner on the TTC.
I met kd lang and playwright Tomson Highway at the Northern Lights music festival.
I saw Britney Spears arriving through the VIP entrance at Madonna’s Drowned World Tour in Philadelphia.
I also met Dar Williams, who is only about 5’2" and gave me a bear hug. I stole her set list off the stage after the show that night. I love Dar.
I saw Jared getting a six inch chicken salad on wheat…
Erin Bruce flew on the same plane as me. Unless you’ve watched the channel 9 morning news in Eugene, OR though, you’ve never heard of Erin Bruce.
As far as subways go, Bernard Goetz took a shot at me one day.
I saw George Will coming up out of the Metro (DC Subway) sometime circa '84-88.
My husband and I were waiting for someone to come off the Concord from London and there was some sort of customs delay. Bored, we started playing that game. There was one guy who looked like Al Pacino and I said that. After a double-take, I realized it really WAS Al Pacino! He had his hair in a cool ponytail, and I found out later he was filming Revolution. He was my favorite actor, but I was too shy to go up to him. (Btw, we were waiting for Kate Bush, who looked exactly like Kate Bush when she finally came out of customs :))
I rode the bus once with the actress who played Debra Winger’s best friend in Terms of Endearment (I think her name is Lisa Hart Carroll). I’ve seen or met lots of famous people, but she’s the only one I shared public transportation with.
I saw Parker Posey & some guy I didn’t recognize get on the downtown 6 train at (IIRC) Astor Place last summer. She looked quite tired and down in the dumps, but then so did every one else 'cuz of the heat wave we were enduring.
It’s not a subway, but I see Randy Savage every other week or so at an area Bennigan’s. And Hulk Hogan loves the TGIFriday’s. Both of them live in St Pete Beach, about 10 minutes from me.
Do you work for UCSF?
No, but I live on Lincoln Way one block down from that stop.
I was in an elevator with Henny Youngman.
I was in a different elevator with the little fat guy who used to host the syndicated FAMILY FEUD, but I can’t remember his name now. The one that Richard Karn replaced. . .Fooey! Why can’t I remember his name???
And I was in a restaurant in Miami when Morley Safer was there.
I met Tom Brokaw in an airport in Montreal.