Yes but not as much as they would be if they were exclusive and zero if they just ended up on the old systems :P. Some people who are interested in the new console will buy if cross-gen games exists. Why would they want to get the lesser version when there is the best version on a new console they are trying to decide to buy? It also stacks up the list of games available on the new system, another good reason to buy. Kind of similar to having backwards compatibility. If the new console can play the old games than you can sell the old one and buy the new one. Obviously this is a much smaller scale concept but if games like Beyond Two Souls and the Last of Us became cross gen then you'd probably see a lot of the core opting earlier for the PS4 than they might have otherwise.

Do they help push hardware? Yes.

The nextgen releases of games like BF4 are going to be the definitive console versions. So that will motivate fans to buy new hardware.

Cross gen titles didn't help Wii U for obvious reasons.

Personally they're just a nice little bonus, I think. At this point I'd buy a console for the exclusives (which would need to be plentiful enough to justify the price) but having definitive versions of franchises I follow (such as Metal Gear Solid) appearing on a next gen system would probably make the deal a little bit sweeter.

They can be. Depends on the situation.

Damn, I did forget about Zelda: TP. It was certainly part of the reason I bought the Wii at launch (the other was Wii Sports and what I thought motion controls would bring to games). On the other hand, the Wii version was not simply a prettier version of the game, it was the motion control that made me want that version.

Cross-gen titles, while by themselves aren't enough to buy a console, they can be a big bonus that increases my likelihood of purchasing a new console. Before I buy a new console, the console would need some sort of incentive that I can't find on current gen systems - be that exclusive games, new features, etc. If a console has what I consider to be worthy incentives, then I get interested. After that, I consider the overall library of the console to see if I will actually spend sufficient time playing the console. This is where cross-gen games come in. So, while they are merely a bonus and not my primary concern, it is possible that such a bonus plus the exclusive content would convince me, whereas the exclusive content alone would not.

Battlefield 4 certainly should be much better on next gen systems. Not only because of the graphics.

So far only that and Watch Dogs would make me get a new console (not counting exclusives at the moment). For CoD and Assassin's Creed I probably wouldn't as I think that they will look, feel and play rather similar to the current gen (or last gen....) versions.

MGS5.... maybe.

if MGS 5 is on the PS4, will probably buy it for the PS4.

to answer the OP's question, yeah it would probably be a reason to buy or to be more precise buy the console at an earlier point

Fairly important. For the core gamers at least.

People know next gen exclusive titles are coming, thats not even a question. But in the past the you would wait until they actually arrived or risk having your new system collecting dust. Instead I can play superior version of ps3/360 titles on the new systems. Depending on the price they launch at, I'd have no reason to wait instead of picking up a ps4/720 this year. I've never bought a console at launch because of the lack of games (exclusive or not), so now that is not an issue I know I'll be picking up a system this fall.

Also, I'd find it difficult purchasing a game I really wanted to play when I know that there is a superior version out there.

For the majority of casual gamers it will not make a difference, but they are unlikely to be early adopters anyway. Some of them will be swayed if PS4 COD and Fifa looks noticeably better.

personally I probably will pick up the next gen version of cross gen titles I'm interested in, but I doubt I'll early adopt any of the systems

I imagine if there are really glaring differences between current gen and next gen versions of these big franchises then it might sway quite a few people to pick up a new system