EVE Online has a free-to-play component that starts November 15. That's in about two weeks. However, were you to start a 14-day free trial today or tomorrow, then you'd technically be getting a jump on EVE Online's free content, since there's a lot of crossover between what's available in a 14-day free trial and what will be available in a free-to-play account.
In theory, your free trial will be ending just in time for EVE Online free-to-play begins. I haven't tested any of this, but developer CCP isn't hiding your ability to do any of this. The 14-day free trial is the first thing you see on the homepage, and EVE Online: Ascension launches November 15.
EVE Online will never die. It's been around since 2003 and it just keeps getting prettier and prettier. There's nothing like it in the MMO space. That's what makes it such a love-or-hate proposition for gamers: because there's truly nothing else like it. Write it off as a "spreadsheet simulator" at your own risk. Or, perhaps give it a shot—free trial and all—and see if the rumors are true. See if it really is nothing more than Excel with spaceships. See if there's really no reason this game keeps popping up in the news, year after year, with reports of massive in-game and real-life wins and losses.
This video incorporates live interviews and cinematic footage, and, yes, some actual in-engine gameplay. I love the quote it opens up with: "This...'game.' You're not ready for it."