Manga Ranma is very intelligent, far more than many people credit him as being; judging by fan fiction.
Ranma's largest problem is that he is a live in the moment type person, which is both a good thing and a bad thing. It's good because he does not dwell on his problems, like Ryoga does, but a couple of consequence from being a live in the moment type person are shortsightedness (does not plan far enough in advance/think things through enough/come up with contingency plans) and impatience (which leads to him to doing things like trying to sneak into the girls changing room instead of waiting until after school).
He has displayed a high level learning ability judging by how fast he learned the Umisenken (Genma only showed him once), Cologne's surprise that he was able to learn the Hiryu Shoten Ha as fast as he did, and he has learned entire schools of martial arts over night (Martial Arts Tea Ceremony). This is even commented on in the manga, Akane for instance does so at the beginning of the Romeo and Juliet arc.
Ranma's manga incarnation appears to be doing fairly well in school even though he has missed at the very least a few months of school (time in China), missed part of that year (school started several weeks earlier), and will skip school (skipped it to go on trip with Happosai, Genma, and Soun during the Konatsu story arc for example). Another thing that shows that Ranma isn't doing all that bad in school, at least in the manga, is that Ranma wasn't worried about Principal Kuno showing Ranma's grade to everyone which implies that Ranma does not generally get bad grades or he really doesn't care about them (a view point that is countered by Ranma's actions when Principal Kuno implied they were extremely low). Ranma was also happy with his grade when it was shown on CMN news meaning it wasn't that bad a grade. Since Ranma does care about how people view him, for him to get very bad grades would be out of character because it would make him look stupid. For those who say that Genma wasn't happy with his grade my view is that Genma was upset about allowing Principal Kuno to put the grades on television (i.e. that Ranma let Principal Kuno get one over Ranma). Miss Hinako doesn't really attempt to get him to improve, she tries to get him to take school seriously and conform.
Ranma is fairly cultured though uncivilized and tends to ignore social conventions though he is aware of them and uses them on occasion when he feels a reason to do so. He did write, direct, and star in a play of his own making to try and get Happosai to change Pantyhose Taro's name. He does display knowledge in other fields besides martial arts such as cooking, sewing, first aid, repair work, CPR, cleaning, designing, etc., and can usually be counted on to know at least something helpful on just about anything. He is generally the person who comes up with a solution or figures things out, examples: figured out that Tatewaki Kuno was the principals son before anyone, figured out the source of Rouge's (the Ashura's) power, figured out that the cursed spatula was actually an iron, saw through Principal Kuno's and Gosunkugi's disguises, etc.
Ranma is very good at making new tactics, copying techniques, developing counters, and discovering a person's weakness. He even had stated that using a technique against him multiple times is pointless. (Happosai used pipe throwing technique; Ranma reversed it throwing Happosai instead.) If you have a weakness of any type Ranma will figure it out and use it against you.
People say Ranma is stupid because he didn't think to jump into the spring to cure his curse but when you consider that no one else has managed to cure their curses it is quite likely that part of the curse is an inability to cure yourself of it. Meaning a cursed individual would not think of that as a possibility until after it is no longer an option. The guide did not appear to know of a cure to the curse at that time Ranma was cursed (or at least did not know of its location). That is one possible reason for him to take Ranma and Genma to Shampoo's village. If the guide did know the location of the cure he probably would have given it to them. The real reason, of course, is much simpler; Takahashi wanted Ranma to be cursed for plot reasons and likely had not thought up a cure until later when she decided that it could also be used for a story arc.
As for Ranma not knowing what Romeo and Juliet is (another thing I've heard people use to say Ranma is stupid). This is not an example of stupidity; it is an example of ignorance. Ranma has spent most of his life training, though he did go to school as well, and just did not learn about it. He was also not the only character that did not know it, Tatewaki Kuno, Gosunkugi, and Happosai were also unfamiliar with it. This is no worse than people around the world not knowing the Tales of Genji (An extremely important and well known Japanese work of literature that every Japanese person knows about and is required reading in Japanese middle schools).
Ranma's inability to play cards in one arc was a result of PIS (plot induced stupidity). That arc was filled with PIS (and is in my opinion the worst arc in the entire manga). He can be seen playing cards with his classmates and not losing at various stages of the manga, both before and after that story arc.
As for Ranma not remembering or thinking about whether he had a mother, remember in the Manga, Ranma was taken from her before he could even walk and almost everyone he knows is motherless (Tendo's, Kuno's, Ukyo, and Shampoo). He most likely just assumed she was dead.
As clarification this post is about Ranma's intelligence not really on how knowledgeable he is. For some reason, I often see people think intelligence and knowledge are the same thing, they are not. You can be intelligent and not overly knowledgeable, they are not mutually exclusive. Ranma has shown to be plenty intelligent but he lacks knowledge (as well as patience) in a few things people take for granted (interpersonal skills in romantic situations mainly). He is a teenager, were he not fictional and capable of maturing, he would gain knowledge and experience which would better enable him to utilize his intelligence.
In my opinion, Ranma is a martial arts nerd that is not overly interested in many other things. He is also pretty pragmatic. The point of the last two sentences is that things like popular culture do not really interest him and he will happily learn anything that has to do with martial arts or that he can see has a practical advantage in knowing e.g. learning the names of every past ruler of Japan or all the baseball teams would be viewed as a pointless waste of time since he'd see no practical purpose for that knowledge and it has nothing to do with martial arts but if it relates to martial arts or he sees a practical purpose in acquiring the skill/knowledge he will happily do so.