For as long as they lasted, and as unique and colorful as they seem to be, did any Egyptian customs, religious ideas, music, or artistic ideas get adopted by other cultures or exist as remnants in modern times? As far as I can tell, none of their ideas, other than mathematical or scientific, had a lasting legacy.
Edit: Thank you for all the thoughtful and thorough answers. I obviously have a lot to learn about ancient Egypt!
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Both Donald Redford and James Hoffmeier identify various Egyptian practices that are present in Biblical Judaism. I have a near-complete list at home, but you'll have to abide by my memory for now.
Many of the names of Biblical figures, specifically those of the Levite tribe are Egyptian. This includes Moses, Aaron, Miriam, Phineas, and also some lesser known names like Hophni and Merari.
The bitter waters ritual appears to be an Egyptian practice (Redford).
Several of the tabernacle features are akin to Egyptian temple elements (Hoffmeier).
Unfortunately, this meager list is all I remember off the top of my head. I'll update when I get home.
Also, possibly of relevance. The Egyptian god Seth is identified with the Canaanite God Ba'al who has many overlapping features with the depiction of YHWH in the Hebrew Bible. It's hard to say who influenced who here though.
Would you mind clarifying the time range? A couple of things come to mind- science aside- but I'm not sure when you'd consider the cutoff to be. 1200 BCE, 600 BCE, 0CE?
There are papyri scrolls on medicine that detail some medicines or practices that are still used today. Such as the Ebers Papryus, which has a passage explaining how one should relocate someones jaw, should it unhinge. The same technique is still used today.