A German goth. Note the heavy makeup, "creative" hair cut and piercings.
An emo guy. Note the band tee, pink belt, makeup and hairstyle.
A stunningly beautiful Victorian goth girl. Hair is center-parted and not completely straight as is common with Victorian goths. Note the cat-eye makeup and and dark red lipstick, the necklaces and dress.
An emo girl. Note the blond hair, sneakers, glove, bright pink shirt that most goths would not be caught dead in, the bow, the hairstyle. Interestingly, the eye makeup and stockings she's wearing are more gothic than emo, but the fact that she's taking a picture of herself at such an angle, her lip color and most of all, her hair make her an emo rather than a goth.
Another goth girl, identifiable primarily by her corsets. Corsets are a very important piece of every goth girl's (and in some strange cases, guy's) wardrobe. If an emo were to put on a corset they would automatically become goth. No, there's no way around it.
A famous emo kid picture. Obviously emo, you can tell by the hair (the cut and style; also, goths rarely have any blond hair, and when they do, it's usually white-blond, not golden blond), the heavy eyeliner and shadow and the picture itself. Goths tend not to take pictures of themselves and this girl is clearly holding the camera.
A goth guy. Although his attitude appears more emo and some of his accessories may very well be worn by an emo, the outfit has altogether way too many studs and spikes to be emo. Also, the netting on his arms is not seen on male emos. Lastly, his hair; absolutely no fringe whatsoever.
My God, he's smiling! Emos tend to smile more than goths; even if it is a tiny half-smile or a full on grin like Kenny The Smiling Emo, the one pictured. Also, goths usually don't wear a simple t-shirt and jeans, they tend to accessorize way more than emos.
For some reason it surprises me it's even legal... anyway, goth has strong connections to the BDSM culture that emo does not have. Goth is more adult than emo; emos tend to be within the 12 - 25 year old range, while goths are usually anything from 14 - 60 years of age.