I can't say if LOTR really changed my taste in movies. Prior to LOTR, I was a huge Star Wars fan (of the original trilogy, anyway...the new ones choked to death on CGI), so that falls into the same sort of epic escapism category, and I already loved The Princess Bride.
LOTR didn't really lead me to any other movies within the genre, though I tend to wind up interesting places when I follow LOTR actors around. Elijah Wood brought me to Everything is Illuminated, a truly unique film that is definitely within the top five on my favorites list. Viggo Mortensen led me to Hidalgo which has served my friends and I well in terms of rainy-day entertainment. Seeing his face on the cover of The Road by Cormac McCarthy led me to discover a bleakly beautiful book. I'm awaiting the movie with bated breath.
I do think I wouldn't have watched Monty Python and the Holy Grail without LOTR's influence. Make of that what you will, as I certainly don't know as there's any significance to that.
I don't care for the special effects revolution that LOTR brought about. There's something about seeing flesh-and-blood people onscreen that no amount of computer wizardry can replace. That said, the special effects in LOTR do still remain the standard by which I judge other movies. So far, only the first Chronicles of Narnia really measures up. Movies need to have a soul, a purpose, beyond special effects, or they're just a disaster, and I hope that cinema realizes that sooner rather than later.