This list is going to focus on standard and sport-standard motorcycles primarily as they are the most versatile categories, and therefore most useful to a new rider.
Honda CBR250R--This is Honda's latest entry into the small-displacement segment. It has sporty styling but with upright ergonomics for a more comfortable and practical ride. It was introduced specifically to contend with the long-time champion Ninja 250R which has dominated the 250cc class for over twenty years. Time will tell how it ultimately fares, but the bike's reception by the press has been excellent. In fact, most reviewers say that the Honda is an overall nicer, tighter package than the Ninja. It's only true loss is in raw power where Kawasaki's twin-cylinder powerplant has the edge over Honda's technologically advanced single. Low end torque is better, but top end is compromised. Still a very nice package, plus it has ABS and fuel injection which are not options on the US market Ninja.
Kawasaki EX250 (Ninja 250R)--The undisputed king of the 250cc sport-standard class is facing some tough competition, but sales are stronger than ever of the insanely fun Ninja 250R. It's level of polish and trim isn't quite on par with Honda's and the technology is a little dated, but that doesn't stop this bike from being a blast to ride. The lightweight design is proven and parts for these bikes (especially the older generations) are extremely affordable. Perhaps most valuable, there is an immense wealth of information about them from maintenance to repair available online. Still unrivaled bang for your buck... For now.
Suzuki SV650--Offered in multiple levels of trim, this is a more refined sport-standard with fuel injection and a fantastically torquey, reliable v-twin engine. Maintenance is relatively easy and the build quality is excellent. This is a very fast motorcycle, so it is only advised for larger riders and people with significant previous experience on two wheels. Many say that it's a great first motorcycle, but it will certainly get you into trouble a lot faster than one of the 250cc offerings listed above. Offered in naked, half and fully-faired configurations to suit your tastes.
Kawasaki ER6-N/ER6-F (Ninja 650R)--Very similar to the the SV650 but with an in-line twin-cylinder engine configuration. The engine is reported to have a similar character to the Ninja 250R but with significantly more power. Specifications are similar to Suzuki's offering as well, though the styling is radically different. Available in both fully faired and naked trim with similar ergonomic differences to the SV650. Naked Standards
Suzuki TU250--This little standard has a particularly classic aura about it with nice highlights of chrome, dual-shock suspension and a bucket headlight. Hidden beneath the retro package though is a very modern (though simple) fuel-injected air-cooled single engine with lightweight and reliable components. With a relatively low top-speed of about 75mph, you may want to consider the somewhat sportier Honda or Kawasaki for long stints on the highway as you'll still have some power left to get out of the way if needed. Still though, it's very economical and easy to handle making it great for riding in an urban environment.
Suzuki GS500--With a similar vibe to the TU250 albeit with less chrome, the GS500 is another time-tested bike that has undergone few major changes over the years. It's proven itself to be very reliable, comfortable and capable for long trips as well as sporty riding. Power comes from an in-line twin that has somewhat muted power when contrasted with the Kawasaki or Suzuki 650 twins, but it is more than ample power for all practical (and some not-so-practical) purposes. This is a good option for larger riders who feel the 250cc offerings are a bit too cramped or sluggish when combined with their body types. The GS500 is unlikely to easily get away from even smaller riders with conscious riding habits, and is more readily recommended for a new rider than the SV650 or Ninja 650R. Enduro/Supermoto
Suzuki DRZ-400/DRZ-400SM--A wonderfully torquey little motorcycle with a narrow chassis, great handling, and excellent reliability. It will take more punishment than most of the bikes on this list (with the exception of the KLR650) and is better than any of them at off-road trail riding due to its light weight and flickable handling. It has all the power you need for on-road action as well, with a 100mph top speed and enough acceleration to easily do power wheelies in second gear. Like any enduro it's strengths don't lie in long distance trips, and for shorter riders it's tall seat height can make riding it very awkward. The SM or supermoto trim fits the bike with street wheels, tires and brakes for tearing up urban environments like a hooligan. Lane splitting is cake with this one! Significantly more power than a 250cc, so go easy on that throttle until you get a really good feel for the bike, then work up slowly. The same goes with any of the larger-displacement bikes in this list.
Kawasaki KLR650--While a bigger and more unwieldy beast than the DRZ-400 (and therefore not as well-suited to tight trails, it will go damn near anywhere, and is by far the toughest bike on this list. Lots of aftermarket luggage options for this bike. Another time-tested design, over 20 years old like the Ninja 250R. The 650 single doesn't make a ton or power or torque and it's a bit heavy, but if you're a taller rider and love off-roading this is a great choice. More suited to dirt than street but capably handles both.
Suzuki DL650/V-Strom 650--With a retuned version of the SV650 engine this is an adventure bike more suited to road than dirt, with less suspension travel and less aggressive tires. Still very capable for the occasional forest or gravel road, but not as tolerant to abuse or bad roads as the KLR650. It's much more powerful which makes for more comfortable highway miles, however.