An entire game? No, but I think it'd be worthwhile to memorize combinations.
Memorizing Games
I work on tactical combinations and these come up in games too. Any other thoughts from folks on memorizing whole games?

Silman(and other teachers) actually encourage us to just(more or less) 'breeze through' reams of games, vs taking 30 minutes per game. I think I saw him say maybe spend 1-2 minutes per game, and try and do about 30-100 a day. Every day for weeks, and even months.
Have you tried the "breeze through" approach? I've heard it meantioned but never talked to anyone who actually tried it.

I tried it the other day(for the first time). I'm just finishing Amateur's Mind, and I'm a little burnt out on reading chess books. So, I was gonna do a few months of this 'breeze through' approach(to give my brain a break, and also to bend my mind in a new direction for a while).
I did 3 Silman games(from chessgames.com's Silman's "notable games"). Obviously, I can't say much(at all ha) about this technique, but I can say, that after only 3 games, my 'chess mind' got bent HARD. I had to quit. It's definitely what I'm gonna start doing here everyday soon. I'ma do 3-5 games a day for 2 weeks(mixed with tactics trainer and 1 correspondence game at a time), using a markoff list for motivation. I'll try ramping it up each coupla weeks. I'm planning on doing it right up into about Christmas time. I'm not training to be a master, I just do it for fun(I love getting stronger, but only for fun), so I'm not gonna kill myself. It really is amazing what just a VERY LITTLE study can do, if you do it every single day for a few months.
I'd love to hear how it goes BigKingBud. I'm going to start working through Chernev's "The Most Instructive Games of Chess Ever Played." I may try a rapid run through first and then go through slowly.
And the morphy opera game is only 17 moves. Maybe I'll memorize it and see what I think.

Anyone had read "Chess novel" by Stephan Zweig? A guy who is jailed in isolation reaches WC level after memorizing 200 master games and then playing himself blindfold for several months.

Silman(and other teachers) actually encourage us to just(more or less) 'breeze through' reams of games, vs taking 30 minutes per game. I think I saw him say maybe spend 1-2 minutes per game, and try and do about 30-100 a day. Every day for weeks, and even months.
I have tried this on numerous occasions. Far from getting to 30-100 a day, I'm fried after about 5 or 6. It's a lot harder than it would seem. However, now that I see it mentioned again, I may give this a shot for a couple of weeks and see if my mental muscles improve to the point where I can do 10 or 15 in a row.
One interesting approach to picking games is to go to chessgames.com, pick the player of the day, and play through his/her notable games. There are always between 5 and 10 of them, so playing them all quickly would give a quick overview of some strong games. Pluse a lot of variety.

Are there any classic games that folks think are so incredibly instructive that it is actually worth memorizing them?
Yes.
I regularly memorize games, both classic and recent, including some of my own. I maintain a list of games that I consider worthy of memorizing.
Usually, when I memorize a game, it stays in my memory for a few months, but then I need a few prompts. There are games--Anderssen's immortal and evergreen games, for example--that I have rememorized several times over a period of several years.
I have found that after memorizing a few games, it becomes easier. Like almost everything you do with your mind, practice perfects.
I have written several blog posts about memorizing games. If we exclude my lack of self-discipline since mid-May, I can claim that I'm currently memorizing most of the games in Rashid Ziyatdinov, GM-RAM: Essential Grandmaster Knowledge (2000).
A sampling of my posts on the subject:
http://chessskill.blogspot.com/2013/03/principles-of-chess-training.html
http://chessskill.blogspot.com/2012/03/memorizing-chess-games.html
http://chessskill.blogspot.com/2012/03/instructive-games-worthy-of-memorizing.html
http://chessskill.blogspot.com/2012/12/soviet-chess-politics.html

@Todd and Msteen
I'm gonna try it for a few months(breezing through), when I get sick of it, I'm planning on starting Silman's "Reassess your chess -4th edition 2010".
I just took about 6 months to finish The Amateur's Mind. Like I said, I do it for fun(or VERY SLOWLY ha), I'd like to be closer to 1800ish by next year at this time, but I really just play for fun.
It doesn't take much for me to get SICK of chess(at least any kind of chess regimen). So, IDK, I doubt I'll be 1800 by next year. But, it's fun just getting the strategies down, and getting better at combinations, day by day, week by week,...

Memorize 5-7 famous games perfectly.
According to cognitive scientists, the brain can remember 5-7 pieces of information. This phenomenon is known as "chunking" theory. So choose 5-7 masterpieces (8 if you're really up to it :) ) and memorize them. You'll remember more and thus be wiser than trying to learn as many games as you can.

i memorize my blindfold games and my OTB long games for a week and then I cant remember the move order anymore, and i dont remember uninteresting parts of the game too
@BigKing
I spend a lot of time just doing tactics. It is a fairly intense regime, but it works becuase I actually enjoy doing tactics. Here's what I'm going to try: as I work through "The Most Instructive Games of Chess," I am going going to run through 5 games in 20 minutes or so. Then go through each of those games for 20-30 minutes each. Then repeat through the 60 games.
@Trash_Aesthetic
Anywhere from 3-10 is what I'm looking for. I'm not going to spend the time memorizing 100 games. Do you have any suggestions for specific games?
@Skotheim
I have worked on memorizing two positions from a tournament last weekend that I didn't play as well as I should have. I'll have to think about memorizing my own games. I don't want to commit my mistakes to memory!
And thank you for the links, Ziryab

I don't like Silman's approach of 1-2 minutes a game. I like the approach of if you have chessbase, set it to 20 seconds per move auto-play. That way you can see the position, think about it and the plans behind the moves. Flicking quickly through a game although probably somewhat benificial is not imho the best way to go through. And of course, you have to analyze games for 30 minutes sometimes.
If anyone could enlighten me how to set the game on auto-play for a set period of time per move on chessbase reader 2013 that would be great.
As far as memoriation goes don't sit down and memorize a game. Remember the key positions, the general ideas, the tactical combinations, the endgame manuevers etc. If while analyzing it you memorize it great! But I don't think you should sit down and say I'm trying to memorize this game today. It's similar to memorizing lots of theory, it can be helpful, but the best plan is to learn the plans extremely well until you know them backwards and forwards.
I really do not like the 1-2 minute approach. Maybe if I gave it a long try I would see the benefit but it just gives me a headache.
I went ahead and memorized the Morphy opera game and my initial impression is very positive. I first looked at it a week ago and was able last night to run through it and explain the moves well. The latter is particular important if this is going to be worth anything.
@CP6033: I agree that the goal is to remember key positions, ideas, tactics, etc. My overall question is whether or not memorizing a few games would help with this. For example, the Morphy opera game has really cemented into my memory the shift of the Q from f3 to b3, castling to bring the rook to an open file, and 3-4 other fundamental concepts. These may seem like an obviously moves to be aware of, but the whole point is the know obvious moves well so that one doesn't forget them! And luckily the opera game was only 17 moves.
My current plan is to try to memorize 1 game a month. Nothing too intensive. Game 2 is the sixth game in Chernev's The Most Instructive Games Ever Played: Mattison vs. Nimzovich in 1929.
I've been working through classic games and following the general rule of taking about 30 minutes/game. This lets me get a sense of overall strategy and basic ideas in certain openings. I obviously remember very little of the specifics of the games later on (which is fine, I think).
Are there any classic games that folks think are so incredibly instructive that it is actually worth memorizing them?