Freud is little read today, but he was actually a very engaging and amusing writer who is a joy to read. And in fact, although we are not generally aware of it, Freudian ideas permeate modern consciousness. Indeed, the very idea of consciousness, and its corollary, unconsciousness, was popularized and concretized by Freud.
Another idea developed by Freud which is pretty widely accepted today is that experiences that happen to us as children affect how we behave as adults. It was a pretty unusual idea at the time, when people were often thought of as born into what they are. It's interesting to see how this concept has worked its way into popular consciousness in a distorted form. Think about the whole discourse of repressed memory. The idea here is that very traumatic experiences in childhood, like sexual abuse, can be repressed - that is, pushed into the unconscious - only to suddenly reappear much later in life, when the memories return. Now I don't in any way want to suggest that sexual abuse of children doesn't happen; clearly it does, and it's abhorrent and disgusting, and should be stopped. But what I do want to point out is that, in Freud's view, what is in the unconscious will continually "speak", if you will, in symbolic form. When something is repressed, it doesn't mean that the horror will disappear for a long time and then reappear wholesale. Rather, the painful incident will constantly throw up reminders in disguised form. That's the point of the slips and the phobias and the neuroses; it's the unconscious reminding the sufferer again and again about what happened. So, if Freud's right (and I think here he may be), repressed memories don't represent truth as such, but rather symbolic representations of past events. So if you suddenly "remember" at 35 that your father raped you when you'd never had any memories of such a thing before, it may be a sign that he was a nasty prick, and did awful things to you like shouting or hitting or taking away your Slinky - all of which you do remember - and perhaps the rape of children has figured in popular discourse, and so your mind renders his abuse to you in a symbolic form which resonates with popular discourse today.
This is just my view of Freud's view, and not the truth, so please don't get too mad at me about it.
Another aspect of Freud's thinking which is still quite influential today is the idea that talking about something will help you get over it. Thus psychoanalysis is sometimes called the talking cure. It makes sense in this theoretical paradigm that talking would help, since talking can render conscious what was unconscious; it un-represses the repressed. In the west we're pretty obsessed with "talking things over", "getting things off our chest", and "clearing the air"; we render everything into discourse. (I didn't find this to be the case at all in Thailand, where lots of things are just never said. People communicate quite effectively, I found, just not with words. That's not our way here in the west. But that's another story.) Now Foucault, who was a better historian than Freud, recognized that the talking cure had a genealogical connection with Catholic confession, and he saw, in a way Freud couldn't, how discourse is a tool of power. But Foucault's ideas about this are rather alien to us today, while Freud's are more familiar and accepted, if only in a veiled way. (I'm not trying to be obscure here, I'm just saying that I think in some way we're all Freudians, we just don't know it.)
Freud had some other ideas that look pretty quirky to modern eyes. Like many thinkers of his time, he was interested in the connection between human evolution and personal development. In Civilization and Its Discontents (a great read, by the way), Freud postulated that, early in human history, people lived in promiscuous hordes. The only biological link recognized at first was that between mother and child - this link being difficult to ignore. Paternity was largely unknown at first. Gradually, the link between sexuality and reproduction became clear, and thus, in a way, the Father came to be. (For Jacques Lacan, by the way, this all became transmuted into the symbolic, so that children learn the Name of the Father as they learn language. But that, too, is another story.)
Anyway, in time people gathered together into simple family groups. The problem is that the boys wanted sex, specifically, sex with their mother. (There hardly ever seem to be daughters in stories like this.) So one day they killed the father so they could have sex with the mother. A parricide! A horrible crime! They were overcome with guilt, (and also lascivious delight at gaining access to good old mom, but that, too, is another story). The point of all this is that sexuality is a dangerous and anti-social power that must be tamed if we are to live together in society. Neat story: father versus son, desire versus civilization, nature versus culture: it's human evolution, and personal development (as Freud saw it) all rolled into one!
Today, it's difficult for us to know how to read narratives such as the one in Civilization and Its Discontents. Did Freud think his theories were factually true? Or was he writing a myth? Or, strange thought, is the distinction between the two a false dichotomy? I suspect that, for a subtle thinker like Freud, the latter is the most likely scenario.
If you want a good read, and you don't mind dense but clever writing, try Freud some time. I think he's great fun.