I would be thrilled if someone told me I looked like Charlize Theron. Until they told me I looked like her from that movie where she played the serial killer. 
I do think telling someone they look like someone else, unless that person is universally thought of as the epitome of beauty or handsomeness, is fraught with the danger of them not appreciating it, even if you meant it as a compliment.
My nephew gets told he looks like Prince Harry all the time. He's more bemused than anything but I don't think he takes it as a particular compliment.
I still remember one woman asking if my best friend and I were twins. No? Then surely we must be sisters. Lady, whatever drugs you're smoking, I want some. (I didn't say that.) Because we look nothing alike. I'm fat, she's skinny; she's a redhead, I'm blonde; her hair is straight, mine's curly; she's at least an inch or two taller than me; she has an aquiline nose, mine's kind of snubbed; she's flat chested, I'm decidedly not. Seriously, we look absolutely nothing alike. But for some reason, this woman was convinced we were twins. We laughed about it over a glass of wine or three later but at the time? It was so weird.
Funny. The same thing happened to me and my former BFF. Twins? Uh, no. Sisters? Not even close. I am 5'9". She's 5'2". I'm blonde. She's a redhead. She's extremely busty, I'm average. Her eyes are green, mine are blue. But someone insisted we were twins. I have a southern accent, she's from the Bronx.
Oooookay.....
Well, not all siblings look much alike...which can lead to entirely different weird and awkward assumptions. My brother and I attended the same university at the same time (undergrad for me, grad school for him). Once he was mistaken for my date: friends saw me at a festival "with a guy!" and wanted me to tell them all about it--their excitement deflated substantially when I clarified "Uh...That was my brother." On another more memorable occasion, a stranger somehow concluded that we were an engaged couple.
It wasn't a question, either--we realized when he referred to my brother as "your fiance."
We never really figured out how he came to that conclusion, considering we were all just standing around chatting, but we both found it rather disturbing.
Onyx, I get that All. The. Time. with my brother too. I've had people call my DH to tell him they saw me "out with some guy", so I must be cheating.
Most of my life I've been told I bear a remarkable resemblance to Soleil Moon Frye. I don't particularly see it, but I guess there are worse people I could be compared to. 
An ex-BF and I used to get the opposite, people were always assuming we were brother and sister. Other than having more or less the same color hair (his dead straight, mine wildly curly), blue eyes and glasses, we looked nothing alike.
Our response to "Are you two brother and sister?" would be: "Sure hope not!" followed by laughter. Too bad this was before Game of Thrones became a pop culture thing, we could have made some excellent Lannister jokes.
My brother and I were once asked if we were newlyweds. We're not a physically affectionate family. It was weird. More often, I'd be heading around town with him and run into some of his female classmates (most of whom had fairly obvious crushes on him). These girls would be incredibly cold to me right up until my brother referred to me as his sister - at which point, of course, they suddenly decided to be my best friend. I wanted to tell them I knew exactly what they were doing, but it was easier to just roll my eyes and let it go.
My other sister and older brother used to get asked all the time if they were da
ting, too (and they're even less physically expressive than my little brother and I) - and now people often assume my sister's husband is her brother, because he looks more like her than the rest of my siblings. It's very strange coming from a family where you don't look much like each other.
My sister and I also hear that we either look exactly alike or nothing alike. I'm thinking some of it has to do with the setting they meet us in, because we get along really well but have very different personalities about some things. My guess is that if you see us doing something we're "similar" about, our mannerisms make us look very alike, but if you see us in a setting where we tend to have opposite reactions to things, we seem like complete strangers.
On that vein (and getting back in the direction of the thread topic), when I get compared to a celebrity, I find it's more often because I'm
doing something that reminds them of the celebrity than because I physically look like them. Most often, I resemble the celebrity in question only superficially (like we have the same hair color and general age range), but I'm emphasizing words the way they do or telling the kind of jokes the celebrity usually tells. The physical similarity is scant, but just enough to support a general comparison. Does the celebrity you're compared to have some kind of noticeable mannerism, habit, or setting in which they're frequently seen? It might help if you can reframe it as a personality comparison.