After seeing the Ranma 1/2 anime series, I was very curious to read the manga that served as the source material for the series, because I know the anime ended before the manga did. Now that I have read through all 36 volumes of the Ranma 1/2 manga series, I can share the observations that I made while reading the series.
The anime depicts the story in the first volume of the manga without any real noticeable difference. I noticed the first deviation between the two mediums when I read the second volume. In the manga, Azusa and Mikado (the martial arts ice skaters) are introduced into the storyline before Shampoo is; however, when the manga was adapted for the anime, these two storylines were flipped.
In volume four of the manga, the character of Gosunkugi is introduced; he is one of several admirers that Akane Tendo acquires over the course of the series. However, Gosunkugi is introduced much later in the anime series. In the anime, a character named Sasuke was created to take on some of the roles that Gosunkugi played in the series at this point in the manga; Sasuke was a ninja servant for the Kuno family. Another difference is that a package that was sent to Dr. Tofu's office in the manga is sent to the Tendo dojo in the anime; considering what is in the package, it made more sense for it to be sent to the dojo. The biggest change between volume four of the manga and the anime is the fact that a martial arts melon splitting contest that takes place on a beach is changed to a snow skiing competition in the anime.
The character of Sentaro, as well as the concept of the martial arts tea ceremony, is introduced in the fifth volume of the manga. However, Sentaro's introduction takes place a bit later in the anime.
When I read the sixth volume of the manga, I discovered that a storyline was told differently between the manga and the anime. In the manga, the stories about the dojo destroyer and Shampoo's herbal remedy are depicted as being part of the same story; in the anime, they were done as two completely different stories. To be honest, I'm not quite sure if I liked having these elements as part of the same story better than as two different storylines.
In the seventh volume, the only real difference I found was that in one of the storylines, Gosunkugi takes an incriminating photo in the manga. In the anime adaptation, Sasuke does this action instead. In the eighth volume of the manga, the character of Ukyo was introduced, and there's also a storyline that involves a bracelet. In the anime, both of these stories take place later in the series than they do in the anime. The ninth, 13th and 20th volumes of the manga each include a story that was not adapted for the anime in any way, shape or form.
Around the time you reach the 21st volume of the manga series, fewer and fewer stories were being adapted for either the Ranma 1/2 anime series or the Ranma 1/2 OAV series. The few stories that were adapted for animation from the later volumes were usually rather close in telling between the two mediums.
It's really hard for me to say whether the Ranma 1/2 manga telling of the story or the Ranma 1/2 anime telling was better. Sometimes, the anime made changes to some of the details, which did help the story make a little more sense; however, this only happened a few times. While the manga could be said to be better because it tells the complete story, I will say at the risk of providing a spoiler that the story doesn't truly end when you reach the end of the last volume of the manga series.