Nami is actually a really good support, I don't really know why people don't play her more.
Her heal is deceptively strong: it can hit three times if you are in the right situation, and it has a very short cooldown, and relatively low cost, it's definitely one of the stronger heals in the game.
Her Q is a long ranged, AoE stun. Need I say more? There are champs with worse ults.
Her E gives damage, slows, and speeds up your allies. That's like support nunu's entire kit!
And her R... I feel like this is the most misunderstood piece of her kit. There are two ways to use it: as a suprise, by casting it from out of sight, as in a bush, in order to initiate, or as a follow up for a already cc'd team (like if you have an amumu on your team).
And her combos...
I like E -> Q-> W myself, but you can also Q -> E -> W if you are good at landing skillshots, and if you already damaged, you can start off by baiting them, then casting W into Q -> R for 6 second cc.
She's kind of a mix between Sona and Alistar: Powerful long range poke and buffs combined with hard cc and healing. The best way to play her is like a shark, circling around the enemy support to harass him with blessed auto attacks and aqua bubble and going in for the kill with tidal wave and deadly flows of water when they slip up.
Nami's kit synergizes so well with so many champs! For guys like Vayne or Kog, she gives them a slow and extra dps to make up for their weak early game. With aAshe and Varus, she can poke champs to death while destroying them when they try to close. And for burst adc like Graves and Corki, she can pin the enemy down with cc while dealing good damage.
Beastly beautiful. Pick her up. She's worth it.