Indeed.
As darkwzrd4 says, there is a stream of evil about. Here's how I see it.
-Mathias curses God, takes Ebony & Crimson stone, defies god. Ebony Stone makes him a Vampire. Crimson Stone makes Death his loyal confidant, Death cannot touch him (I forget if I have my stones mixed up).
-FAN ADDENDUM: It is my belief that the stone that makes him a vampire makes him have a pact with an ancient demon, Chaos, who resides in another dimension. Either that, or in the events of Castlevania III, when Mathias, now renamed Dracula, declares his war on humans, makes this pact (before, during, or after his defeat as he dies).
-Since then, the power of Chaos rules over Dracula's more violent side. When the 100-years milestones happen and the power of the evil in humans' hearts is at worst, Dracula has a more powerful but more chaotic disposition when he's resurrected. He may not remember anything aside from "destroy all humans" or "humans are to be your prey". Whatever humans he kills or feasts on power both him and Chaos.
-When Dracula is resurrected prematurely, Chaos's power, since it's powered by the evil in people's hearts, is not as strong within Dracula. As such, he's able to remember some memories and/or glimpses of his previous escapades.
Let us examine the times Dracula remembers the Belmonts (and any others) properly:
-Dracula is able to remember Trevor, to a degree, in Curse of Darkness (as Isaac, no? It seems he does).
-Dracula is able to remember Christopher to a degree, in Belmonts' Revenge, otherwise he would not have taken his son. There is no dialogue in the game to confirm this, though it is implied as why would someone who has no new memories bother to mess with the Belmonts specifically?
-Dracula is able to remember Simon in Simon's Quest, because it seems that Dracula put the curse on Simon AND had the foresight to both know that a Belmont would come to him and that he would get another shot at defeating him.
-Dracula is able to remember the Belmonts in particular, in Harmony of Dissonance, though he doesn't know Juste personally.
-Dracula is able to remember the Belmonts in Rondo of Blood, specifically coming after Richter's Girlfriend Annette, as well as Maria Renard. He is more destructive in this reincarnation.
-Dracula is definitely able to remember his own son Alucard, as well as know who Richter is, in Symphony of the Night. Dracula is ridiculously prematurely resurrected in this one, so he seems to be at his most 'human' upon his defeat.
-Dracula is able to remember the Morris clan upon his premature Moon-Ritual resurrection in Circle of the Moon; a premature resurrection done shortly after another premature resurrection, with no game of its own. In THIS reincarnation he even notices the character's aging.
-Dracula remember no one in Castlevania64/LoD, as the bad guys are doing a ritual similar to the Ritual of the Eclipse (more on that later), which separates Dracula's Soul and puts it on Earth. This Blank-Slate Dracula (as Malus) remembers no one right know, but knows he's the lord of the Castle.
-Dracula remembers every Belmont, as well as side characters like Shanoa, Maria, and others, in Judgment. I believe THIS Dracula is the least Chaos-corrupted, but the most human-arrogant one. "You seek Chaos? Look no further!"
It seems the Ritual of the Eclipse separated the power of Chaos from Dracula's soul. Thus, Soma, Dracula's reincarnation and another chance at redemption, is the least corrupted version of him. Chaos's power is not completely gone though, as it seems to beckon to him, to come forth to the Shinto Shrine in 2035 in the events of Aria of Sorrow.
The Power of Chaos is able to immediately corrupt Soma by tapping into remnants of Dracula's old memories. Specifically, the death of Elisabetha and Lisa, and use them to turn Soma into Dracula and completely lose his will to be Human. In AoS, he was able to control the Chaos. In DoS, depending on whether you get the pendant in the Garden, you can see this manifest itself in its entirety.