your opponent didn't use his time correctly and deserved to lose.
Blitz Chess Etiquette
I understand it's OK if your opponent was in time trouble; if that was in fact the case, it was bad etiquette from him/her to make a draw offer.
A major part of blitz chess is clock managment. On Chess.com, I usually play only 5/0 games, and I look to the clock to be my ally any time I can. Sometimes I will make bad sacrifices, like giving up a rook for a bishop, knowing full well it's a bad long term move, but with 18 seconds left on the clock, he won't be able to capitalize on it before his time runs out. Other people do the same to me. I consider it part of the game.
I think of Blitz Chess as a somewhat different game than "real" chess.
The amount of charity you might show really depends on the time control you started out with. With bullet/blitz, you are essentially calling him on his poor time management, as previous posters indicated.
However If this was a classical time control and an epic battle ensued, perhaps some courtesy would be in order. :)
Even so, some players play with courtesy at any and all time controls. These players deserve praise for sportmanship.
Other factors also make a big difference as well. Is it a tournament game or just a club/social game ? Is your opponent a friend or someone you dont like ? Is your opponent stronger, weaker or roughly equal to you ?
I recall once having a rook and pawn ending that was a "book" draw but I could have run my opponent out of time if I wanted as he was under 1 minute ( for the game ) and I had about 10 minutes left. He offered me a draw hoping I would do the "honorable" thing and give him the draw. There was a crowd of people around our board and they were waiting to hear my response as much as he was..... what would you do ? 
A win is always better than a draw. We were both contending for first place in this event and meeting on one of the top 3 boards with 2 rounds to be played after this one.
Flag him and take the win, I suppose. You earned those 9 extra minutes on your clock because you had a more efficient thought process that included better time management. How many of us spend our weekends going to tournaments to "make" friends? I think that's more of a pleasant side-effect than the motivation.
Though if there was a draw offer that resembled the picture below ...

I wouldn't take the draw offer. If it's a book draw, he can just play the moves, no problem, even with a minute on his clock. This is especially the case these days where he would have a 5 second time delay, which might not have been the case in your game.
If he has to take time to think about the moves, it's not clear that he should just get a draw because someone else knows how to draw the position. I've seen masters win drawn rook endings. Just because it's a book draw doesn't mean the other guy knows how to draw it. (I've personally won from losing rook endgames.)
If I've already not been making progress, and he's playing the correct defense, I would agree to the draw.
Well, I prefer to give a draw rather than getting a win in such a position (R+K vs. R+K) and of course the scorn of all the players around. It is a game after all ...
If the position is not so clear, then I would play on, *even* if the outcome is well-known theoretically. For instance, I would play on in a R+K vs. Q+K ending even against a 2200+ player up to the end.
I decided to give the guy the draw because it was more important to me to win friends and the respect of the other chess players here than to gain the extra half point. I also gave the draw because I like the guy I was playing, there are several here that I do not like and I would have flagged them without remorse.
Well, I finished 2nd in the event and the guy I drew finished lower than me, he lost one of his last 2 games where I scored 1.5 in the last 2 and finished .5 point behind first.
In the greater world of chess and the chance to get into certain tournaments, on given teams, publishing opportunites, etc. making friends and winning respect is important.
You have to remeber that wonderful American saying
What goes around, comes around,
When it happens to you come back and tell us how you felt.
Sceadungen, I think most people have been on both sides of this. I know for me that when I am in time trouble it's my own fault. If I run out of time, that's my fault too.
I also play tournament games with a 5 second delay. So in tournament games, I'm never going to get flagged in a K+R vs. K+R situation. As for blitz games, the best policy is to just play the next one, don't get hung up on a single game.
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I was playing a 10 minute blitz game on Live Chess today. it got to the stage that my opponent and I each had a king and one rook. Although technically not insufficient material, in general this would be a drawn position. But I was ahead on the clock. So when my opponent offered a draw, I declined, and won the game on time. Was I ungracious? Should I have accepted the draw? Do othrs have similar dilemmas?