The Mega Man Battle Network series is the fun-loving younger brother of the Mega Man franchise. It has the youthful feel and colorful design of the original series, but the games play in an entirely different manner. Most people consider the series to be Capcom's response to Pokémon, but that seems overly cynical to me, and it too easily dismisses what is interesting about it. The Battle Network games are more like a traditional Japanese RPG with the twist of a unique battle system and with grindy leveling replaced by grindy collecting.
Basically, you play as a kid who interfaces with the internet via an avatar, referred to as a navigator or navi, that is Mega Man. Mega Man is a separate sentient being from Lan, the main character, which is probably explained in the story. It is something of a retelling of the original Mega Man series story, but abstracted through Ghost In The Shell-type ideas. So, you run around town jacking in to various electronics, exploring networks and the internet. Random battles are explained as viruses, but the more important battles are against the navi of other characters in the game.
|Typical Battle Network nameless NPC derpface.|
The battle system is what is interesting about the series. The battlefield is separated into two halves, one for you and the other for your enemies, and each side has nine spaces to maneuver within. At it's base, the battles are about moving out of the way of enemy attacks while getting in your own. Simple enough, but it gets complicated when you factor in the different battle chips, which you use like a deck of cards. Battles revolve around choosing the right chips for the right situations, and timing attacks properly. There are swords for close range, buster shots for long range, and all sort of other things.
The choice of chips is also based on the different environmental effects on the battlefield. For example a tile with grass can slow your movement, but it can burned away with a a fire-based attack. Battles end up being very fast-paced and exciting. In spite of the series being aimed at a younger crowd, the games slowly build into being quite technical, and near the end become a surprisingly skill-based affair unlike other portable RPGs.
I would suggest people try out the series, but I certainly would not recommend people play every game in the series. They are all pretty much the same with different stories and locales. I played the Blue version of 3, but I don't think it really matters which you play. There are six games in the series, so maybe you would be better off with later title where it had become more complex or refined. There is also the Mega Man Star Force series, which is something of a sequel series to Battle Network and from what I can tell is mostly the same as well.