For Nintendo, this year's E3 wasn't just about the Wii U: the noise made by its new console tended to obscure the fact that make-or-break time is approaching for the 3DS, and the Wii isn't quite dead and buried just yet. Nintendo was keen to showcase games for its existing consoles, and we got our hands on two efforts that ought to drive 3DS sales – Mario Kart 3D and Super Mario 3D – plus The Legend of Zelda: Skyward Sword, which, despite its tardiness, is surely the most hotly anticipated Wii game ever.

Mario Kart 3D

Pretty much every Nintendo console has launched with a version of Mario Kart, so it was a tad surprising that the 3DS didn't. But the four courses that made up the demo version of the game we played at E3 gave an inkling of why Mario Kart 3D hasn't arrived yet. Rather than being a mere warmed-over 3D-ised version of Mario Kart for the DS, Mario Kart 3D actually has some new stuff in it.

That isn't to say that all the old stuff isn't there, too: it's a reassuringly familiar game, and its perfectly judged mechanics (such as drifting round corners and piling on the opposite lock for a speed-boost) have, wisely, not been tampered with. But one difference becomes apparent the moment you dive into your first race: you can customise your kart by picking from a selection of bodies, wheels (some of which jack your kart up like a monster truck) and glider-wings for the rear.

That's right: in Mario Kart 3D, when you launch your kart off one of those characteristic cliffs or jumps, a wing opens up, and you will glide back to earth. We discovered that speed-boost power-ups work in mid-air, and there's a delightful trade-off between staying in the air and thereby avoiding ground-based traps, and getting back to earth as early as possible, which is usually a slightly quicker way to proceed.

Another innovation is the ability to drive underwater – in previous versions of Mario Kart, there were plenty of water's-edge tracks and, if you ended up submerged, you would be fished out and replaced on the track. But in Mario Kart 3D, when you go underwater, your car sprouts a propeller, and you can drive normally.

Plenty of work has gone into Mario Kart 3D's tracks – while some feel familiar, albeit with new additions, the majority of the ones we played were new. Some featured multiple paths, with thin tracks, requiring precision driving and providing the best short-cuts. There were rolling boulders to be dodged, and a Donkey Kong-themed jungle track – unfortunately, crashing into the DK barrels, we discovered, didn't yield any power-ups. The bottom screen showed a top-down map, so you could keep tabs on competitors: up to eight people can race against each other, either locally or via the web. Although the stereoscopic 3D made it marginally easier to judge distances and aim green shells accurately, it couldn't really be said to have added much to Mario Kart's classic gameplay.

Super Mario 3D

Nintendo development guru Shigeru Miyamoto recently described Super Mario 3D – Mario's first starring vehicle on the 3DS – as a cross between Super Mario 64 and Super Mario Galaxy, and the four levels we played at E3 confirmed exactly that. Its name doesn't really do justice to its originality: Super Mario 3D is definitely not cobbled together from bits of old Super Mario games.

Gameplay-wise, it veers more towards Super Mario 64's classic 3D platforming – there isn't too much messing around with gravity, which of course is characteristic of Super Mario Galaxy. But there are a lot of elements familiar from the latter, such as rhythmic tiles which appear and disappear. One level involved making your way through a pirate ship, avoiding slow-moving bullets and the like, and moving into and out of the screen at regular intervals. Moving in and out of the screen was a recurring theme, and that is one area that is much easier to judge when you play in 3D.

We also had a go with the Tanooki (raccoon) suit, which transforms Mario into a raccoon with a tail-attack (which can also be used to hover). We took on a mini-boss – one of Bowser's younger relations – and had to whack him with the tanooki-tail until he was dizzy. And we saw a new type of block, which, when you bash it, teleports you to an otherwise inaccessible part of the level. Super Mario 3D, given that it is all-new, will be a must-buy for 3DS owners.

The Legend of Zelda: Skyward Sword

You can't help thinking that, if the first Wii-specific version of what is surely Nintendo's most revered franchise – The Legend of Zelda: Skyward Sword – had been ready in time for Christmas 2010, the Wii's disastrous late-period sales dip would at least have been delayed. As it is, the Wii's successor has already emerged, with what will surely be the Wii's swansong still months away.

We were able to play three levels of The Legend of Zelda: Skyward Sword at E3, and were convinced that it will have been worth the interminable wait. They were clearly designed to demonstrate how the latest iteration of the action-adventure franchise makes full use of the Wii Remote's motion-sensing capabilities.

The first level was a bird-riding one, with a hint of Quidditch to it: in competition with three AI-controlled characters, we had to chase a bird and grab a golden statue it was holding. Moving the Wii remote changed the bird's orientation and shaking it encouraged it to flap its wings and speed up. We discovered that the best approach was to fly above our target and swoop down on it. Although this clearly wasn't representative of core gameplay, it was quite fun and showed the game's diversity.

The second level, set in a castle, was much more familiar Zelda fare: Link was on foot, and had to battle spiders and skeleton enemies, the latter using his sword and shield (swinging the Wii remote for sword-slashes and thrusting the Nunchuk to employ the shield). The spiders were best attacked with bow and arrow (with the Wii remote and Nunchuk working together cleverly to ape a bow), and there were also access puzzles to solve, for which Link used his flying beetle to trip switches and open doors. Classic stuff indeed.

The final level on show was a boss-battle, involving just swordfighting, but as we were taking on an elf-like boss, a precise and tactical approach was required, to get around his defences and find unprotected areas to attack. Again, this was classic Zelda gameplay, and the responsiveness and controllability of Link's sword was very satisfying. In its graphics, Skyward Sword harks back to earlier Zelda games, eschewing Twilight Princess's more realistic look in favour of a fairly cartoonish approach. If you're thinking of buying just one more game for your Wii, The Legend of Zelda: Skyward Sword will surely be it.