The NES was the first home console that many people had. Some people have their old NES system still and it plays. Others may have found they have the system but it does not play. I have known people who even have all the old games for some reason but not the system. With used game stores in most big cities and the Internet it is now easy to find old games for the NES for only a few dollars or less. If you do not have your old NES system though you can still play those well loved games.
The first option of course is to get an old NES console. If you do not have one you can find one online at places like ebay. If you get one on ebay or have your own I would suggest you also buy a 72 pin connector on ebay or somewhere else online. If you replace the one on the machine with the new one you should be able to play games every time with no problems. It might not be the same as when you were a kid and had to blow, or clean the games but it sure is less of a headache.
There are plenty of new NES console systems out there. In fact it might be cheaper to buy a new unit then the old one. The quality of the new units vary with most playing better then the original NES because they are top loaders. However some cheap versions are not well made. You can check what is available on Amazon to see reviews to see what system is good. You can buy on Amazon, ebay or elsewhere. Often these new consoles play multiple systems. Most often you can play SNES games as well. Ocasionally you can play Sega games. The one drawback many systems have is that you only use their controllers or a SNES controller. That means you can not use peripherals like the power pad. Some systems also do not work with the Game Genie so if you have one and planned to use it beware of this.
There are now many portable devices that will play NES games. Most of these play roms. Some even come with some or even all the NES games installed so you do not have to illegally download any roms. There are a few that actually play the cartridges. The cartridge kind are a bit silly and awkward though. These systems do not let you use the controllers or multiple players though. Most do hook up to a TV and even have game genie built in. Many of the systems do double duty as mp3 players as well. Unfortunately many are poorly made. The Dingo A 230 is a bit expensive but high quality system that also plays other roms. It might be worth the extra money for the better quality.
Overall what you will get may depend on what you have as well as what you want. If you have an original NES then other then not being able to get lots of games by having roms using the original is the best as it is cheaper, gives you more nostalgia, may rise in value over time, and will play all games and peripherals. The portable ones do allow you to get literally hundreds of games and do more then just be a game system, they also give you portability. The new systems work better normally and are less expensive if you have to buy one but they often can not give the full experience. The choice is yours.