Whenever you talk about big game players the answer will will always be slanted towards offensive players. It's the glory positions and that one goal is the easiest to remember as time passes. I don't believe in clutch or big game players. I believe in consistency. If you are good you are good. If you are great you are great. If you are not you are not. There are a lot of good choices on this list but the big game player has to be Schmeichel. In all situations he was consistently great.
See, that's why I made the statement about being important and being a big game player. Cantona's goals were vital - but were they big games? Big Players are different from big game players. Of our current team Ronaldo and Rio are our biggest game players because against top opponents their play is improved they "step up." One could argue that in his time here Rooney has been more important than Ronaldo, but there's no question as to who plays better when we're facing a top 4 club or in a final or playing in the CL.
Veron...? Rio Ferdinand apart from a few games, one in which he was toasted by the best striker of this generation, or one of... (Ronaldo) he did reasonably well. Especially in big games for us in the league and in Europe (apart from Madrid) and partially Milan second leg. What about him?
Is Keane suffering from performing as well in the smaller games as he did in the big? Remembering some of his Ireland games as well, he was a force of nature no matter who the opposition were. I'm a bit bemused by the number of votes that Solskjaer's getting. Other than the '99 final, I'd have to look up any (let alone the many that would justify winning this accolade) big games where he made a definitive contribution. I'm sure that's partly due to me not paying as much attention as you guys, but offhand I'd place him below the likes of Giggs, Schmeichel, Stam, Scholes, Irwin, and maybe Yorke & Cole. I can't comment on Cantona, Bruce et al. since I didn't watch their primes.
Rio was toasted when we played Chelsea last season, Real Madrid few years ago, and he wasn't that good against Milan either. And the last 2 were pretty much the only big games we had in Europe lately. As far as Cantona - when you think back to the mid 90s and all of our greatest games, Cantona was the inspiration in almost every one - the great derby in 93, FA Cup in 94, including the final against Chelsea, 96 game against Newcastle, which won us the title, 96 FA Cup final against Liverpool, 97 against Porto, etc.
When you think big-game, the first name come to mind is Cantona. However, he never did establish himself in European games based on what thing I read & what I vaguely remembered (specifically I remember Cantona missing chances in our home leg vs. Dortmund...) Like many previous posters has mentioned most of his great big games were in domestic league and cup play. So I voted for Giggs who always seem to step in up in big games... a few moments that stood out: 1) Tying goal away vs. Arsenal when we won the league last time. 2) 1999 CL semi 1st leg injury time equalizer vs Juve. 3) THAT goal vs. Arsenal in FA cup. This is only a few, i am sure there's more. But the three moments I list covered Domestic League & Cup and Europe...
I think the Ole situation is similar to Cantona. Ole scored many VITAL goals that became clutch performances but its not the same as stepping up your play in an important match. They both are/were great players who proved their worth time and again - but it doesn't mean they were big game players.