Hi, just joined, so am joining this discussion late:
My wife got me to read this series (and is making me read the Twilight series next... the two have absolutely nothing in common) and I'm very glad I have. It's very authentic, very rich, and the characters grab you like few in (let me qualify this) fantasy fiction do. As alluded to above, though, try not to get attached to any of them...
I loved (almost) every minute of it, am very frustrated with how long it's taking for the fifth book to come out -- books four and five take place in parallel, and the problem with that is that I'm going to have to wait many years to find out what happens after the fourth book, if you know what I mean -- and recommend the series without reservation. But having said that, here are my concerns, most of which have been at least touched on already:
It's a lot of work. I personally am not put off by Martin's verbosity, but it is a long, dense series, and you have to put up with characters you wish you didn't have to a lot.
It is never. Going. To. Be. Finished. At the rate it's taking the fifth book to be finished and to come out, anyway.
To me, it's in the series' favor that no one is off limits, but yes, you will be upset several times if you slog your way through the first four books. And something short of death happens to one of my favorite characters near the end of Crows, and as I said, it will be years till the sixth book is out and I can find out what happens to her. So it's a bit frustrating.
The books devote chapter-length sections to selected characters' points of view. Each of the first three were limited to a select half dozen, eight, nine (it's been a while) characters, the fourth had quite a few more. But more than once during the series you will stop reading because you get to a chapter "about" a character you don't care about, or find yourself wanting to skip it. The format serves the series well but challenges your patience at times.
It is never. Going. To. Be. Finished.
If you start Game of Thrones I predict you will be engrossed enough to finish it and want to continue. Just be aware of some of the pitfalls of the slow development of the last few books, the format and the capricious way Martin seems to dispose of some characters.