2008 - Never. I probably didn't even have ME1 then.
2009 - I played ME1 but I don't know how much. Maybe more than one playthrough.
2010 - Hyped up for ME2, got it and played the hell out of it. Forget when I got the DLC.
2011 - Played a lot of ME2. Really got in to the whole save transfer thing so I think I played both games. This was all on Xbox though so I don't use those saves anymore.
2012 - Hyped up for ME3, got it and played the hell out of it. Got all DLC ASAP. Played some MP. Then moved into getting a PC version but I don't think I dived into it just yet.
2013 - Finished the DLC and got into my PC version of ME3 and played a lot of that. Also got more into MP then before, but always casually (I still don't play past Gold, if that).
2014 - While ME for my personal playtime has slowed to a crawl, I started to have a friend over so she could play her own Shepard. This is a project that's now over a year, and we've only gotten approx 40% through the trilogy, making it seem like we won't be done until next year (ME4 then? haha). MP time continued, but ended with DAI's release more or less.
2015 - I haven't been playing for myself, but continued to have my friend over for ME. Played DAI instead.
2016 - I hope to have my PC playthrough done and all 'established' in my memory, and potentially, if I get into things enough, have at least a couple more Shepards also done (a different male and a female). Ideally, I'll have 5ish other Shepards but that sounds kinda crazy for me. Want to be ready for the next game.
My Xbox version had a FEW profiles, even though they don't matter anymore. I had a male Paragon, but also a male Renegade alt and a female Paragade alt. My PC canon playthrough will be a near replica of my Xbox male Paragon (Vanguard, more Paragade in ME3).
I guess you could say I've played the Mass Effect 'a few times', and played singular games of the trilogy 'several times'. So not obsessively, but certainly avidly.
I may dive into the games for up to hundreds more hours (if I make more than one profile) or at least tens more hours (if just my canon) once Bioware actually, really announces the next game. The countdown will basically be on.
TLDR; Almost never. But ready to get right into it again in prep for NME, and I have a friend visit once every couple-to-few weeks to play it. Don't know whether I'll be able to stomach just my canon playthrough, or up to 5 more after it.