I've done a bit of looking around and took multiple views into account when I came up with I believe to be a good dual-definition for harem.
1. A harem can be defined purely as a guy just being surrounded by 2+ girls (love interest is debatable).
2. A harem can also (and more commonly) be defined as a man surrounded by 2+ girls who are in love with him.
A reverse-harem would be the opposite of #2.
Personally, harems are my favorite anime as the make me laugh and fanservice brightens my day. Now, while usually the lead male and his ladies are very much the same from one series to the next, each has a shining moment or element that sets it apart. Most generally also lack a reasonable story but there are some out there (Tenchi Muyo, Love Hina, Sekirei). My other harem suggestions, for those who like the genre, are Maburaho, Samurai Harem, Tenchi Muyo: GXP, and Negima!.
Minato from Sekirei is different than Keitaro from Love Hina. Minato is actually really smart and is willing to make bold moves to protect those around him. I find him to be one of the best harem protagonists I've seen.
Well Tom it seems you still have yet to experience a "real" anime harem. But don't worry, there are classics in that genre as well. A couple examples (that I know and love) are Love Hina and Tenchi Muyo. I did a Beginner's Guide a few weeks back for the reverse-harem Ouran High School Host Club to bring some light the the series (and it's the only reverse-harem I know).