I was going to speak to something similar last night, but I didn't want to ruin the vibe.
As a poor growing up, we rarely got to see the Rangers in person or on TV. Hell, I recall one of my earliest "great" sports moments was a night in which the Rangers/Red Sox were on national TV. I think Clemens was pitching. We were down 2-0 in the 8th. Someone hit a 2 run homer in the 8th; someone else a 2-run homer in the 9th. (One of them may have been Geno Petralli.) Point I meant to make was that I listened over 90% of the Ranger games during a 10 year period from about age 7 - 17.
Anyway, thinking back, I realized that I was a fan w/o any expectations. I knew they weren't going to the playoffs, much less the WS. I don't ever remember being heart broken by a Ranger result. (I was extremely insulated from the 2011 WS living in Knoxville.) Going back to @Beau Vine 's quote, there was a year in which Jeff Russell made the All-Star team. My friend's tv went out just before the game started, so we hightailed it to the Promenade Shopping Center in Richardson and watched the game through the front window of a tv/electronics store.
My favorite memory of the Rangers was actually due to another team. Some of you old timers might recall a pitcher from Brownwood, then UT, by the name of Jerry Don Gleaton. From what I understand, my grandfather was a father-figure to him and coached him into high school. One year he was pitching for either the White Sox or Royals. We got seats just behind the 3rd base dugout. He ended up pitching in relief and tipped his hat to me when he got on the mound. Awesome times.
Sorry for the tl; dr. I'm loving hearing everyone's stories and wanted to add my own.