Clearly, the anime does not cover the whole story. One of the major plot points in the whole series is the execution of the plan to eliminate homo-sapiens by the research facility, which involves spreading the virus through a large population by using a missile. We could say that this is half of the whole story and the anime only covered the first half.
The relationship between Lucy and Kouta is very similar in both the anime and the manga. The major difference is the fact that Kouta is a bit more agressive regarding avenging his father and his sister, but in both cases he still tries to protect Lucy (not forgiving her though).
The bridge incident (the ending of the anime) also differs slightly. Mariko does forgive her father and engages Lucy in a battle. She uses the explosives within her to attempt to kill Lucy (thus, her father actually survives and is not killed). She fails and Lucy merely loses her horns.
There obviously are a bunch of characters not introduced in the anime. Most of them are not critical for the storyline, though, which might explain their exclusion at first.
One of the biggest discussions regarding the anime is whether Lucy died or not at the ending. Technically, from the point of view of the manga, the answer is no - she actually survived the bridge incident. She loses her horns, which disables the "evil" Lucy and keeps her as Nyuu. The horns grow back, however.
At first, it doesn't seem like the anime is capable of continuing, since they killed Mariko's father (whose name I forgot), who plays rather important roles through the rest of the manga. This is fixable though, they just need to do a few tweaks and make a new scene where he somehow survives the bridge explosion.
So, yes: the main difference is the fact that the anime only covers half of the story, and kills some people who shouldn't have died.