Mechanical effects of love
If you want to really sell and promote love in your game you can help re-enforce that idea through some customized mechanics. Many players identify much more strongly with quantifiable values rather than abstract emotional ideas. Some games already include mechanics for love and motivation, while others have systems easily adapted. Here I provide a small selection of love based rules for several of my favourite role-playing games. Most of these mechanics will benefit from having the players pick a specific number of people/places/things that they love, usually from 1 to 3 at the beginning of the game, but it can vary from campaign to campaign.
Pathfinder/ 3.5: Both of these systems have a hero point/action point variant option already in place. The easiest adaptation is simply to allow the players to gain an extra point they can use only when acting in the name of a strong love. Alternatively you could allow the players to receive a +4 on an attack, save or skill check as long as it relates to protecting and furthering their love.
World of Darkness: Love can be used as an excellent addition to the Vice and Virtue system. Consider allowing the regaining of a willpower when protecting or impressing someone's loved one. This mechanic is exciting because it's not just when they're in danger, it can also be for trying to impress them or improve your relationship. This means it functions as a virtue, but also a vice. Even lying to make yourself seem better to the person you fancy might qualify for a willpower point, provided of course that lie can blow up in your face later.
DND 5th edition: his is a pretty easy one to guess. Fifth edition really only has one major bonus to apply, and that's our friend Advantage. Consider allowing a player each to get advantage on any one roll as long as it relates to something their character loves and values. This system is extra easy to implement since a 5th edition sheet already has a spot for bonds and allies and allegiances, making it a snap to define who is or isn't an acceptable loved one.
Savage worlds: Another easy system with a great built in rewards system. Give each player one extra special Love Bennie that they can use only in situations relating to their character's love. Simple, easy, and encourages the players to have their characters feel strong about someone or something.
Mutants and Masterminds: Another great system with a built in hero point system. Simply reward an extra hero point when someone's loved ones are in danger and watch the heroic expressions of love unfold.