This game is widely regarded as the best Castlevania game to reach the United States. Why, you ask? First off, you aren't limited to a linear path -- after certain levels, the path forks, and you can choose the path you take to Dracula's castle. The other major factor was the fact that you could play as multiple characters (spirits, as they were called.) They shared the same life bar, but each had their own special attacks. For instance, Grant DaNasty could jump very high, change direction in mid-air, and cling to walls. Sypha was a wizard who had a weak attack, but the special weapons that were available were cool (a powerful flame attack, an ice spell, and lightninh bolts that bounced around the screen.) Alucard, (Dracula spelled backwords) had an attack slightly longer than the whip, and could also turn into a bat. Of course, the main character is Trevor Belmont, who is just like is great-grandson, Simon.
In the Castlevania instruction book, it mentions that Dracula was "looking for another fight after 100 years". You can assume that this is the first time Dracula was being fought. Thus, this game takes place before all of the other Castlevania games. The gameplay is more like the original Castlevania, i.e. more action oriented than adventure, as in Simon's Quest. The basic play mechanics are the same.
The graphics are slightly better than either of the previous two games, allowing constant vertical scrolling areas and some neat graphics. The music is all wonderful, as in pretty much all Castlevania games. The length of the game, and the replayability, is what makes this one of the best Castlevania, in my opinion...Once you beat it taking the forest (treking through a pirate ghost ship, and up a tower), then you can play it again, taking the swamp route, meeting Alucard, and ending up in the castle's basement. And there are four different endings, depending on who your companion is (I never beat the game with Trevor alone, however.)
Read the Castlevania 3 instruction manual!