Strikefleet Omega is a pretty darn good game that is free, though the in-game purchases can get you.
The story is much like Battlestar Galactica: you're the only major combat ship left, all the rest are lost in a huge ambush, and you need to travel the stars, and save humanity, sorta.
The idea is you are a hybrid "carrier" that has a couple fighters, and it will make more as they're lost. You need to protect the carrier from the incoming fighters from the bad guys. You can also put in support ships, such as escort carriers (more fighter groups), mining ships (mine asteroids for fuel and such), and gunships (fires flak at enemy fighters and bombers). The ships can be upgraded as well. You can have up to 6 support ships in a single battle, but you need to spend "currency" (can be mined) for them.
Some of the really good ships you have to spend $$$ on, and I do mean real money. You buy the red credits with real money. Some of the best ships cost red credits. You can also use red credits to buy "perks" which improves your ship or fighters or miners for a single mission. You start with like 10 red credits (you can buy more), don't spend them on frivolous stuff!
Enemies come in waves, from all directions, and you need to move your fighters so they'll take out all the incoming attackers. You can think of it as a "juggling" puzzle as you try to balance various commitments. Protect the mothership, protect the miners, kill bombers, protect the support ships, etc.
Definitely give it a try!