Origin Access is EA's subscription based service that provides early previews of new games, discounts on all purchases done via Origin, and most importantly, full access to a whole bunch of games found within the "Vault". The service is normally priced at $5 per month or $30 per year, but for a limited time you can give it a free try with the newly introduced seven-day trial. You can find everything you need to know about the free trial over at the official website.
As for the games themselves, you can find a full list of what's available over at Origin. But as the Vault has grown in size the list has become fairly unwieldy to read, so here's a slightly smaller list of what I consider the most interesting games in there:
• Battlefield 3
• Battlefield 4
• Battlefield Hardline
• Crysis
• Crysis 2
• Crysis 3
• Dead Space
• Dead Space 2
• Dead Space 3
• Dragon Age: Origins
• Dragon Age 2
• Dragon Age: Inquisition
• Dungeons of Dredmore
• FIFA 16
• Mass Effect
• Mass Effect 2
• Mass Effect 3
• Mirror's Edge
• Mirror's Edge: Catalyst
• Star Wars Battlefront
• The Banner Saga
• The Sims 3
• Titanfall
The seven-day free trial offer will only remain available for a "limited time", though its currently unknown how long that will actually be. So if you're interested in playing the Mass Effect series before Andromeda finally arrives, make sure you take EA up on this offer as soon as possible. Enjoy!