Chobits
I really enjoyed watching Chobits, though I can't easily explain why. It's a well-executed romance with likeable characters, but what's really refreshing is that Chobits doesn't rely on the ridiculous confusions and misunderstandings that drive too many romantic comedies, nor on random coincidences interrupting the revelation of important plot information (Cardcaptor Sakura, I'm looking at you). Or maybe it's just that Chii is really cute.
Hideki is upset
Hideki is suspicious
Chii is happy
Chii is surprised
Chobits has its flaws, to be sure. Among them are the apparent obsession with okazu and attendant offensive sound effects, as well as the seemingly random and inconsequential introduction of Jima and Dita— they're interesting characters, so it's all the more shame that they don't actually end up doing much of anything. Finally, the part of the ending that doesn't relate directly to Chii and Hideki's relationship is a bit hard to swallow: even if one accepts that such a thing could happen, it would have huge implications, none of which the show bothers even to consider.
In the end, though, Chobits is strong enough as a romance that its weaknesses elsewhere didn't matter to me. I liked most of the characters, especially Chii, and I enjoyed seeing her relationship with Hideki develop. If that sounds appealing to you, give the show a try.
By the way, I noticed that nearly every episode of Chobits has a title of the form "ちぃ [verb phrase]," like "ちぃ 出かける," "ちぃ 買う," and so on. Looking back, I saw that all seventy episodes of Cardcaptor Sakura begin with either "さくらと" or "さくらの," and surmised that perhaps this parallel title phenomenon was a Clamp thing. However, I then discovered that every episode title of Magical Girl Lyrical Nanoha ends with "なの"! There must be some sort of conspiracy at work here...