I played them all to completion using Wine. That was back in the 1.3-1.5 days and there were some slight issues, but nothing game-breaking. I remember ME2 crashing like crazy on startup (apparently it did that in Windows, too, so...), but once you got it running everything was fine. There was a display problem in a vehicle section in one of ME2's DLCs, fixed by disabling an effect in the options. That's about it.

They're excellent games, you should play them. ME1 is somewhat different from 2 and 3 (some say worse - I don't agree), but it's still full of win and should be experienced to fully appreciate the series.

Edit: I know it's a late answer, but there were no others.

In my case works

System Specs

Lastest Nvidia Drivers if is possible
Linux Mint 17.2 Raffaela XFCE Edition 64Bit - Kernel 4.0.0-040000-generic (ubuntu mainline)
CPU: INTEL Pentium G3258 (Haswell 22nm) at 4.1Ghz + Artic Cooling Alpine 11 Plus before a Pentium G3220
MEM: 8GB DDR3 1333 (2x4) Patriot value (dual channel: 21.3 gb/s)
GPU: Zotac Nvidia Geforce GT630 (GK208 28nm: 384 Shaders / 8 ROPS) Zone Edition Passive Cooling 2GB DDR3 1800Mhz 64Bit (14.4Gb/s)
MAINBOARD: MSI H81M E33

View video on youtube.com

View video on youtube.com

View video on youtube.com

^_^

I have all three mass effect games working perfectly under wine. I think playonlinux has scripts for them but they didnt work for me. In the end i used wine 1.7.46 and just installed the few dependencies mass effect wants. Which off the top of my head were dx9, vcredist2010, annnnd nvidia physx? All of which are available on playonlinux and wine tricks too id assume. I did have a wierd issue with mass effect 2 and 3, where it wouldnt start or run properly outside of a virtual desktop. So i just re-enabled the virtual desktop, and set its dimensions to my screen resolution. That way its fullscreen and you dont notice the virtual desktop.

They're well worth a play though, awesome games, good replay value too. Also they took the Mako out after mass effect 1. That probably means nothing to you now, but it will :p. I hear a lot of people didnt care for the Mako controls.

First game is probably in my top 3. I play it every now and then. Outstanding OST too. The other two... well, better shooting games though much worse games overall.

I have the series on Origin, is there a way to install the client on Wine and from there the games? I've seen some tutorials on youtube but don't seem to work for me. Any joy for you?

Thanks!