A weird confluence of individual factors that wouldn't be terribly noteworthy on their own.

Part of the reason she's as well-known as she is probably has something to do with the fact that she's a she. World history, particularly in antiquity, is filled with men in leadership positions. Having a woman occupy such a position, and in such a relatively powerful place like Egypt, is atypical. That makes it interesting.

Another part of the reason is that Cleopatra VII lived at one of the most famous periods in Roman history. Her reign corresponds to the tail end of Julius Caesar's reign (with whom she had a son) and overlaps the three major Roman civil wars of the time (plus a few less well-known civil wars). She also had an affair with Mark Antony, with whom she had five children. Antony's attempts to essentially gift large swathes of land to their children to rule as de facto independent kings was ultimately what triggered the final civil war -- the one that ended with the pseudo-independent Egypt crushed and integrated, the Ptolemaic dynasty all but extinguished, and the death of Mark Antony.

Because she was not only around when all of the above events were going on but actively participating in them, Cleopatra is rather hard to separate from the waning days of the Roman Republic. If you talk about the last civil wars before Augustus solidified control, you have to talk about Mark Antony. And if you talk about him, you have to talk about Cleopatra. Similarly, any work of fiction that covers this period will almost inevitably feature Cleopatra in some regard. She shows up quite often in HBO's Rome, for instance.

Compounding all of this is the fact that the Ptolemaic dynasty was... just kind of weird. By Cleopatra's time, the reigning monarchs of Egypt were typically siblings or cousins (Cleopatra herself being, according to modern definitions, a product of incest), resulting in a family tree that is basically a vertical line. We also have, over the course of about 250 years, 15 rulers named Ptolemy and 7 named Cleopatra -- that kind of naming frequency is very unusual in the historical record, even within individual dynasties. They were also Greek, being one of the diadochi dynasties (and one of the longest-lived), and thus somewhat more likely to have Rome pay attention to them. We also know a great deal about Ancient Egypt purely because of them; the famous Rosetta Stone (not to be confused with the language-learning software of the same name) dates to the Ptolemaic era and the Greek text on it was extremely useful in translating Egyptian languages.

There are more reasons that probably influence this, but I think you get the idea.