The Bite-Sized series of articles is meant to take the most powerful cards in Dominion and give a short explanation of what makes them powerful.
Vampire’s strength comes from the fact that it does several different things for you. In many decks you build, you’ll be able to make use of at least one or two of Vampire’s three capabilities: gaining, attacking, and trashing.
The ability to gain a $5-cost card without spending an action is not common, but is very powerful. The combination of this plus the fact that Bat trashes cards, push you towards gaining a Vampire the first time you hit $5 in a lot of cases. Be advised, though, that Vampire/Bat’s gaining and trashing together make it difficult to increase the size of your deck over time.
Bat’s trashing is fairly slow to get online, you have to hit $5, then play your Vampire, then play your Bat. In addition, without any draw it can be difficult to line your Bat up with things you want to trash by that point, making the trashing part one of the weaker abilities of the Vampire/Bat duo, but still nice to have in most situations. Similarly, the hexing attack will sometimes not have a huge impact on your opponent, but is almost always nice to have in addition to the other things Vampire is doing for you, mostly gaining $5-cost cards.