Ada slinked into Resident Evil 2 as a completely different character than we were used to. Like Leon, there was just no comparison between her and the rest of the RE characters who came before her. She was strong, confident, self-reliant, and extremely smart. This is more than we can say for Jill (who habitually needed rescuing from Barry and/or Chris and displayed very little confidence in her abilities) or Rebecca (who spent most of her time being absolutely terrified). Ada was calm and calculating. She knew exactly what she was doing and exactly what she would do next.
Ada came across in RE2 as a little too cold. She wasn't above manipulating or using people to get what she wanted. Her whole relationship with Leon in the early parts of the game was based on her goal to get a sample of the virus. She didn't care about him or anyone else. However, over the course of the game, Ada's hard shell begins to slowly crack. Revealed under her harsh exterior is a vulnerable woman. A human woman. Her emotions got the better of her, and she began to care for Leon. That wasn't part of her carefully laid plans. It didn't factor into her goal. And yes, her affection for Leon is what led to her downfall in RE2. However, it was also a great source of strength and courage for her as well, as she bravely attacked Mr. X in order to save Leon in the end (this was in scenario B, in scenario A, Ada basically gives up her ultimate goal of acquiring a sample of the virus rather than hurt Leon to get it, and is shot when she lowers her guard).
Something I need to mention here is that Ada (at least in RE2) had something of a bad reputation among fans. She was viewed almost as a "slut". This stems from the fact that she was romantically involved with Leon, and yet she was also supposedly involved with an employee of Umbrella named John (she calls him her boyfriend, and he apparently cares a LOT about her as he uses her name for a password in the original RE; yes, Ada was mentioned in the first game). She finds out he is dead during RE2, and takes the news rather well. Therefore there is some debate over whether or not she was just using him to get information on Umbrella (this seems very likely). Still, some fans were a little iffy on her speed in switching to a new love interest. There was also some fan speculation on her relationship with Wesker (who she was working for throughout RE2, and who also saved her after she seemingly died). His own reports indicate that he was not happy with her growing relationship with Leon (I'm of the opinion that he was more concerned about her accomplishing her goals, but perhaps he had other reasons as well?). Personally, I think she was just doing her job, and Leon was the first man that she really fell in love with.
In RE4, Ada's personality is drastically different. She is no longer cold and hard, but rather flirty and playful. She helps Leon out, leaves him little notes, etc. It almost seems as if she is playing with him, and views him as an amusing toy. Personally, I think she is still a very calculating person. She's just found better ways to present herself. She also seems to have discarded the part of herself that grew emotionally attached to Leon so easily. Yes, she apparently still cares about him, but she seems very guarded, as if she views her past actions as a mistake or a weakness. In the end, she still comes through and ultimately saves Leon, though I don't think she so blatantly disregarded her own life in the process as she did in RE2. Is she stronger now? Or, under the flirty facade, is she even more cold than before?