Especially now with DVDs, Netflix, etc., you can spend hours plowing through a TV show, one episode after another. But do you think this has a negative effect on your ultimate enjoyment of a show? Generally, television shows are weekly and when you watch an episode when it first airs, you have to wait a whole week to find out what happens next. It might suck having to wait when you're excited, but it gives you a while to really think about the episode and wonder what happens next. When you binge-watch shows, you might not give each episode a chance to really "sink in" and think 'Did I like that?' 'Did I not like that?'

For example, plowing through a season of a show like Lost can't really compare with watching it as it happened when it first aired, in my opinion. Part of the fun of the show was talking to other people about their theories or critiques. And usually, if you couldn't wait until next week, you could watch the episode again, which gave you a better understanding of everything going on and stuff you might have missed.

It's really tempting to watch one after another, but I feel you kind of miss something. What do you guys think?

I've often thought this. I watch a lot of TV on my computer and sometimes I wish I could have watched shows when they aired originally. For example, I was watching "Deadwood" but ended up losing interest because I couldn't really follow what was going on in the show. If I had a week between episodes to digest and discuss the show I'd probably have had a better experience with it. Then there are shows that are completely ruined through "binging." Typically these are shows which follow a formula instead of long form storytelling. For example, I love the "Batman: The Animated Series" show but when you watch the episodes back to back it gets redundant. Batman meets a bad guy, Batman beats the bad guy. It's the same thing every time but if you have a week to get pumped up about Batman kicking some bad guy butt than it's still a great experience.

I think it depends on the show.

I actually don't watch TV shows that often, but shows I watched through "binging" are Death Note, Prisonbreak (Season 1) and Weeds (also Season 1). Each episode is different, a lot happens in each one and the plot is always advanced. I was perfectly content to watch them that way.

An example a show I prefer to watch on TV in episodes, is CSI and CSI Miami, since the story line is not necessarily linear, just a different crime for each episode. It's kind of boring to watch them solve crimes over and over again with only a small amount of actual plot. I prefer to see one episode at a time.

I think it's beneficial to watch some shows in this fashion.  I have caught up on so many shows this way and now get to experience the best of both worlds (no that I'm fully caught up).  As for not fully understanding a show, I had this problem with Game of Thrones (Season 1) because I was unfamiliar with most of the characters.  After I would watch an episode I would read the recap on IMDB so I could comprehend everything and then watch the next episode right away.  I think that is a nice substitute for the "wait a week" effect.

I'll begin by saying I prefer not to binge watch TV shows but I don't think it is a bad or good thing.
The good side of binge watching is that shows have to become more like movies (quality wise) to build a strong reputation so people make the decision to binge watch it. Also shows have to stay consistent and make sure to tie-up all the loose ends because it is far more obvious that a show has forgot about a character if you are watching it back to back.
The bad side is that shows can jump the shark much faster since they have to keep the viewer's attention for seasons at a time and it's hard to think of new interesting stories. Another problem I've found is that shows will start by concluding the story from the last episode and the episode will end in the middle of a story, this drives me crazy! Why can't each episode be a self sustaining story that is itself interesting, instead of just another strung along story that doesn't really go anywhere! 
I would recommend binge watching comedies since they are usually one story one episode and dramas can string you along a bit too much, so if you want to binge watch a dram I would recommend finding the best season and seeing how you like that before watching the whole show.