When I had shorter red hair, everyone used to tell me I looked like Gillian Anderson. At one of my jobs everyone called me Scully.
The only other person I’ve really been compared to is Shirley Manson (from Garbage), but I don’t think I look much like her any more either.
I don’t really think I look like anyone specific now.
This is embarrassing to admit, but around the time of the 1992 elections, when she and I were both awkward teenagers, I got told I looked like Chelsea Clinton. Happily, by the time I was nineteen, most people switched over to telling me I looked like Tori Amos. Now that I have short hair, though, I really don’t think I look like anyone in particular except myself!
When I was thinner I was told on a daily basis that I looked like Charlie Sheen. The first thing my wife ever said to me was “you know who you look like?”
When I was in my early teens it was Sean Penn.
Sometimes it was billy baldwin.
I’m often told that I resemble Emilio Estevez’s older, heaver brother.
Scary thing is, I see it too…
Christina Applegate and Mira Sorvino… allllll the time…
I am told all the time that I’m a dead ringer for Briana Banks, a porn star. I do admit that in the face, we look remarkably similar, with the exeption that I don’t wear as much makeup. I also don’t have the ridiculously large implants she does. I’d post a link to a picture, but I don’t there are any of her clean enough to link to.
No one really, at least not now. A while ago when the movie first came out, I was told I looked like Sonya Blade from Mortal Kombat.
Now? No one. Except for multiple people throughout my city. I have never met one of my twins but they are all over Winnipeg 
I get Claire Danes, Gillian Anderson, and Courtney Love all the time. My current boyfriend is the first one to nail all three without being told about 'em; most people only get one of the three. I get Gillian Anderson a lot more when my hair is freshly dyed the fire-engine red I love it to be (I call it “Scully red”).
I bear some resemblance to Melissa Gilbert. she’s just a year older than I am.
People even called me “Laura Ingalls” when I was in jr. high because I wore my hair in braids back then.
I always get either Ben Affleck or Billy Zane. Don’t see it myself (other than the tall-with-short-hair thing), but there ya go.
Several times: Meryl Streep.
More times than I could ever count during a time in which I was heavier: Hilary Clinton. This disturbs me for a number of reasons, but dealing with the appearance aspect only - I am younger, so there; even at my heaviest I was smaller than she; Hilary has malocclusion, whereas my parents went to great effort and expense to ensure that i would have perfect teeth, and I make every effort to maintain them. But I have to admit, I could see it myself - a younger, thinner, perfect-toothed Hilary.
One time only, alas: Rebecca DeMornay.
Yeah, I gotta say you do look a lot like her. Although, I have to say, from recent pictures of RLC, I think she’s a little bit chubbier…
When I was younger, I was told I looked like a young Liz Taylor because of my eyes.
Unfortunately, now that I’m older, I seem to be looking like an OLD Liz Taylor. 
My husband was approched by a stranger in a bar who said he looks like Dave Matthews, which is funny because when I started dating him, I described him to my friends as looking like Rob Schneider from SNL. He definitely looks like a cross between the two.
Maybe a little like Ann Curry from the Today Show.
When I was in college, I was told more than once that I looked like Kyle MacLachlan of Twin Peaks fame. That doesn’t happen so much now, though.
When I was young (about 6-10) and I had dark brown hair, I was very often told that I resembled Danica McKeller (of The Wonder Years fame) and Christina Ricci. When I got a little older, about 14, I was told I looked like Katie Holmes, Yasmine Bleeth, and Mariah Carey, the last of said comparisons puzzled the ish out of me. Since going blonde, however, I’ve been compared to Britney Spears and Madonna (with an observation that maybe I looked a little like Angelina Jolie). The only one I personally believe might be true is Yasmine Bleeth (if I had dark hair) and Britney, presently. Someday I’ll post a pic.
Forgot one. Recently I’ve been compared to Reagan Neis from Maybe It’s Me. That one I tend to believe too :).
I’ve been told I look like a brown-haired Britney Spears.
Who aged terrbily.
Then had acid thrown in her face.
And was in a tragic car accident.
And then there was a fire.
Yeah…maybe not quite that good.
Eh, I’ve had several people tell me I look like Carson Daly… I argued that it was merely the fact that I always have about 3 days of stubble on my face… My friends insisted that I really do resemble the guy.
Novus
When I’m in the States, I am told that I look like Eric Stoltz. When I’m in the UK, I am frequenlty told I look like Kenneth Brannagh. Maybe I’m somewhere in between…
But, a few years ago when Earl Spencer was in the news when Princess Diana’s died (he is her brother), I was living in London and I was told that I looked like him a few times a DAY!
I’m thinner than he is, but I can see the resemblance.
Odd this should come up. I was just musing about this the other day.
Several years ago, I was told I looked like David Byrne (Talking Heads) more than once. I never saw the resemblance.
However, I have been struck that I somewhat resemble one guy treated as a minor league sex symbol for a while - let me explain:
Also several years ago, I was looking at a photo of myself, and was struck with a resemblance to Paul Darrow - British actor probably best known as “Avon” from “Blake’s Seven”. I wouldn’t have seen it, except that I happened to have a very “Avon-Like” expression on my face and wasn’t wearing my glasses.
I’m older than that now, have visibly aged, and put on some weight. The other day I went digging around for a more up to date photo of Darrow to see if I still think I look like him. Well, kind of:
http://www.avon-paul-darrow.co.uk/biography.htm
That bio shot doesn’t have a date on it, but is similar to other shots on that site showing Darrow at some fan function last year. Actually, he doesn’t look bad for 60.
And, no, I’m not going to provide a mug shot of myself at this point to allow people to tell me how off base I am. Apparently, I look like David Byrne. OK. I’m closer to him in age anyway.