At the end of "Tango," new on Yabla this week, Mélanie Laurent sings:
Parce qu'au fond tu l'aimes bien, elle te manquerait je crois
Because deep down you really love her, you would miss her, I think
Cap. 52, Mélanie Laurent: “Circus” & “Tango”
When you're talking about missing someone in French, manquer is the verb to use. However, in this context, manquer actually means "to be missing" rather than "to miss." Though elle te manquerait might appear to mean "she would miss you" upon first glance, its literal translation is actually "she would be missing from you," which is just another (perhaps more romantic) way of saying "you would miss her." So when talking to someone close to you whom you haven't seen in a while, make sure to say tu me manques ("I miss you," literally "you're missing from me") rather than je te manque ("you miss me," literally "I'm missing from you").
On the other hand, manquer does mean "to miss" when you're talking about missing something in the sense of not being there for it. In this context it's synonymous with the verb rater:
J'ai manqué [or raté] le bus.
I missed the bus.
The expression "manquer de + infinitive" (or just "manquer + infinitive") means "to nearly do something." "Faillir + infinitive" has the same meaning:
Il a manqué d'être tué [or: Il a failli être tué].
He was nearly killed.
But in the negative, this expression more often means "to not forget to do something":
Ne manquez pas de vous arrêter au numéro treize de l'avenue Junot
Don't forget to stop at number thirteen Avenue Junot
Cap. 12, Voyage dans Paris: Butte Montmartre
Another common meaning of manquer is "to lack," usually in the expression "manquer de + noun":
L'hôpital manque de moyens, comme toutes nos formations sanitaires, hein?
The hospital lacks resources, like all our medical facilities, huh?
Cap. 22, Le Journal: Hôpital ultra-moderne à Burkina Faso
In fact, the noun form of manquer, un manque, specifically means "a lack":
J’ai compris qu'il y avait un manque énorme au niveau, euh... alimentaire
I saw that there was an enormous lack at the, uh... alimentary level
Cap. 7, Alsace 20: Mangez bien, mangez alsacien!
Finally, manquer is also used in the impersonal expression "il manque + noun" ("x is missing"):
Il ne manque plus que l'argent nécessaire.
All that's missing is the necessary money.
Cap. 6, Il était une fois - Les découvreurs: 13. Stephenson - Part 6