Congratulations on getting engaged!
I wear my engagement ring and my wedding ring on my left ring finger, and on my right ring finger I wear the ring my husband proposed with. (He wanted me to help choose my actual engagement ring, so he got me a ring with my birth stone in it–amethyst–for the actual proposal.)
Sometimes I trade out the right hand ring for a different one for a few days.
I only take my rings off when I’m painting (oils–would be hard to clean plus harsh chemicals).
One – my wedding ring. Any more than that and I’d lose any real man cred that I have at the pub.
One plain gold band - my third wedding ring (only one wedding - I lost the first ring and outgrew the second one.)
Wedding ring, engagement ring. I have some other nice rings with stones, but I wear them only occasionally, seldom to work as they throw off my typing. Not that they make it difficult, but just having something “different” that I don’t wear every day.
Another Canadian engineer checking in (it’s the only ring I wear).
And yeah, if I’m ever bored in public I play ‘spot the engineer’; highest concentration of engineers I’ve found in a non-engineering setting is at intermission at the Stratford festival.
Heh. I had to have my original wedding ring “stretched” at a jewelers because I ordered it half a size too small to start with. I was amazed – they did it with a whizzy machine while we waited, watching, and it didn’t visibly change in any way I could see. But PING! it fit.
4 for me: engagement and wedding ring on ring finger on the left hand. On my right hand, currently ring finger and little fingers, but will be moved to middle and ring when the last of my baby weight is gone: a wishbone with diamonds which my husband gave me on the birth of our first daughter and an emerald-and-diamond which he gave me on the birth of our second. All are white gold or platinum, I don’t like yellow gold on my skin. I never take the wedding ring off, the others go on when I leave the house.
I like to joke that the reason I went back to school for this degree is for the BLING. I was rather jealous of my husband’s Iron Ring It’s amazing how much a couple bucks worth of stainless steel has made me happy! 
I play this too. So far, a Habs game has won, followed by airports (though a lot of engineers travel for work, so maybe that doesn’t count?)
Only a wedding ring. Plain gold band. Low key.
Heh, I’m much more likely to not be wearing the very nice and very expensive watch I got for graduation than my ring. And I’d probably miss the ring more if I lost it 
Half the fun is trying to come up with reasons you’re seeing more or less engineers than random chance would predict.
For example I’ve never seen one at my local supermarket. Am I too busy looking at the shelves to notice or do none of their spouses trust them to shop? There are plenty of engineers in my city, they have to be getting their food somewhere.
Three. Gold pinkie ring on my right hand, Celtic-design silver puzzle ring middle finger left, silver ring on my left thumb. These are rings I’ve been wearing for years.
We’re trying to decide whether or not to have my engagement ring resized smaller. I’ve lost weight since the wedding and a couple of weeks ago I was in a store and my engagement ring just fell right onto the floor, off of my hand. That scared me. However, I don’t know if I’m at a stable weight or if it will go back up, so we’re debating.
Usually I wear no rings.
When I wear rings, they’re silver only.
On occasion I wear a skull ring on my middle finger and tribal ring on my ring finger. Or I wear a wrench ring (cast from a Craftsman sparkplug wrench) on my middle finger and one that says “In Aeterna” on my ring finger.
Left hand: little finger, my mother’s family ring, with our birthstones in it. Ring finger, a simple sterling silver braid. Right hand: little finger- the ring my mom got for her 16th birthday. Ring finger- a sterling silver Gordon Setter ring.
One on my left hand (my wedding band) and three on my right: on the ring finger, middle finger, and thumb. I pick one up every time we go to the Renaissance Faire. Next will probably be the pinkie.
It’s zero right now. When I was married, I wore a wedding ring.
3 = Left hand, wedding ring, engagement ring. Right hand - another ring just for the fun of it.
One wedding ring. Keeping it low key.
I wear a claddagh ring on my left ring finger, a silver puzzle ring on my left middle finger and usually a garnet (my birthstone) ring on my right ring finger. Sometimes when I change up jewelry for dress, I go go with a gold, silver and lapiz ring on my left pinky finger and one gold ring or another on my right ring finger. The claddagh ring is the constant one.
My partner and I agreed that we would not wear matching rings until we can legally marry in this state. Probably not any time soon.