Advance Wars was a great series of lightweight strategy games for the Game Boy Advance. The games were attractive and easy to get started with, and yet there was some meat to them too. Best of all, you could play most of the battles in about half an hour. They were perfect for "I want to do something fun for a little while, but I don't want to spend all night on it."
There were three games in the series: Advance Wars and Advance Wars 2 on the Game Boy Advance, and Advance Wars: Dual Strike on the Nintendo DS. (There was also Advance Wars: Days of Ruin on the DS, but it was done by a different team, and it sucked.)
I replay these games every couple years, and I always enjoy them, but I haven't found much else that scratches the same itch.
Super Robot Wars was the closest thing to Advance Wars, but I don't like it as much. SRW is IMHO overcomplicated, and is basically a strategy RPG. You spend more time leveling up your units than you do playing, and grinding and leveling up is far more important than placement of units and use of terrain.
I tried one of the Fire Emblem games and didn't like it. Like SRW, it seemed like it was more about leveling up than battlefield strategy, and giving all the characters names made it unpleasant to lose them in battle.
I also played Valkyria Chronicles on the PS3, which I loved, but it tends to be a game you play for hours, rather than a quick pick-up game. VC2 on the PSP was the same way, only worse, and VC4 on the PS4 was good, but had a less enjoyable storyline.