Okay, so I know this is meant to be a semi-casual thing and some people are going to take offence to this thread. To those people, I apologize. My playgroup is full of sharks and people like to break things, and then we congratulate them and ban the combo if necessary.
Today I ran across an Eversor upgraded with a 2 damage Neuro-gauntlet and the Flip Belt crusade relic allowing him to redeploy 9" away from enemy models each turn instead of moving. With 10 attacks on the charge thanks to various character Battle Traits he was a serious menace.
Another very powerful combo I saw is using the Auto-Loader weapon upgrade in concert with Sororitas miracle dice. You can put a combi-plasma on the Sister Superior in every squad, then use your miracle 6s to automatically hit safely with overcharged plasma and get a second auto-hit shot free thanks to the weapon upgrade - and each shot can do 3 damage.
I know people were worried about the Artificier weapon upgrade (6s cause mortals) on a Punisher Tank Commander too, though I haven't seen that in action yet.
Beyond specifically strong combos, there are some general trends as well - the strength of character upgrades really incentivizes you to run combat characters from day 1, and the weapon upgrades encourage you to run units with upgrades for 1 model or the sergeant (i.e. Intercessor Power Fists, Tyranid Warrior Venom Cannons, etc.)
Anyone find anything else really cool?