Though sacrifices are "required" by Vayikra (Leviticus), with the fall of the Second Temple, Jews stopped making sacrifices. Why did they stop? One simple answer is that there was no longer a Temple at which to sacrifice, and no longer any priests to do the sacrifices.
A common interpretation is that prayer rose to fill the void left by sacrifice's departure. Personally, I have not yet figured out how to motivate myself to pray. So part of me wishes we still had sacrifices, because maybe I could get on board with that more easily than with prayer.
I hope this suggestion, which is only partly serious, will not offend anyone. But I fear it might. For one thing, many Jews believe that Temple rites should not be practiced again until the Messiah comes and the Temple is restored.
Also many Jews would object to killing animals for the purpose of sacrifice. I tend to agree, so I would suggest that modern sacrifice only be of the "meal offering" type. These consist of the flour of some type of grain, oil, salt, and sometimes frankincense and myrrh. Can you imagine what that would smell like? I can't; that's part of why I want to try it!
The idea appeals to me for various other reasons. I imagine that it would be outdoors, and would engage all of the senses, except in cases where the offering is burnt completely in which case taste would not be engaged. We have a fair amount of flame in Judaism in the form of Shabbat and Chanukah candles, but here we could have a legitimate fire, which can be a powerful, primal experience to make and to watch. I love the deep respect for words embodied in Judaism, but the non-verbal nature of a meal offering made over open flame appeals to me as a complement to all things verbal in the tradition.
The existing rituals that come to mind as somewhat comparable are those surrounding Sukkot. The outdoorsy-ness; the physicality of building the sukkah and shaking the lulav. So perhaps what I should do is resolve to observe Sukkot in those ways, rather than make crazy, possibly-offensive suggestions about reviving 2000 year old rituals.
