The generally accepted figure in the publishing and photographic industry is 300 PPI. It's like a mantra in the imaging world - hi res = 300PPI. However, this tells very little of the real story of resolution and image sharpness/quality. It says nothing about the quality of the pixels in an image, just the amount of them.
The key issue with sharp prints is real resolution. How much fine detail is actually in the image, as recorded by the camera or scanner, or originated by the image maker in digital production. And how much of this true detail can be actually expressed in a print. It's also important to separate detail itself from apparent sharpness (i.e. edge definition), as poor use of the unsharp mask so often demonstrates that fine detail and apparent sharpness are two very different things.
The first thing I would say is that . Firstly, there is an unreasonable and unwarranted obsession with sharpness in photography, very often to the detriment of the images made by pixel peeping obsessed photographers. Sometimes pin sharp images just aren't required, so do try and remember that composition, message and expression always trump technical perfection. A fair percentage of images simply do not rely on fine detail in any critical way to achieve their expressive goals. So don't let your obsession with sharpness put you off making big prints if you want to.
Most images do although benefit from fine detail, especially when viewed for extended periods. Fine detail rewards the eye as it moves through the image, and allows your image to work more successfully when viewed from closer distances. Fine details give your image greater longevity and dimensionality, particularly with landscapes, as it can increase realism and draw you in to an image.
The first and most important thing that will affect your image's sharpness, and also its quality when enlarged, is your photographic/image creation technique. No amount of fancy lenses or more megapixels will save you if your basic technique is poor, or if you create a low-res file in Photoshop rather than a hi-res file to start with.
The rule is simple - always scan, work and render at the highest resolution your system allows. With scanning, a good truly sharp scanner that produces an optically sharp 600 PPI scan is enough for most purposes such as reproducing to the same size as the original or up to double, and 1200 PPI is enough to capture all possible detail off original works for larger reproductions.
There are several things to master.
The old photography rule of being able to hand hold at 1/ focal length is fine for adequate results with small prints - for instance, if using a 50mm lens, then you can only hand hold reliably to 1/60th of a second. The reality is, however, that even when using a 35mm camera with a 50mm lens, there will typically be an obvious visible difference in sharpness between shots taken hand held at 1/60th, 1/125th and 1/250th.
Fundamentally, using a faster shutter speed will always result in a visibly sharper image, and most people over-estimate their ability to hand hold their cameras. There is no substitute for steady support, so the first step to take is to always shoot from a stable platform, such as a tripod, if at all possible. If that is not an option, aim for a faster shutter speed if possible. Image stabilisation, while very handy, is not nearly as effective as actually keeping your camera still, so don't rely on it too heavily if you're aiming for big prints.
The second most important thing that will affect the final resolution of your image is focus and depth of field. With small camera systems, it can be very hard to focus properly because basically it is very hard to see your subject through a small hole.
In any picture, there is only one flat plane of absolute focus. Areas in front and behind this plane of absolute focus may appear acceptably sharp through depth of field, but are not truly in focus. When calculating what is 'acceptably' sharp, many people use systems like hyper-focal distance, circles of confusion etc. While these are useful aids, be aware that most of these systems/tables were created long ago when imaging systems and lenses were of lower quality.
Film and digital have come a long way, as well as lens design with higher quality lenses, and so modern systems are capable of capturing and printing far higher detail than ever before. With this in mind, the goal should be to take advantage of this higher recording ability, and to use a greater depth of field in most situations. Blur is easy to add later, detail lost however is lost forever. Many will tell you that you should avoid low apertures due to refraction issues. I strongly suggest you test this as you will find this is, 99 times out of 100, internet mythology. Softness due to lack of depth of field is almost always worse than softness due to diffraction.
The third determining factor is the quality of your recording system - the quality and size of the system you are using to capture your image. Basically, bigger pieces of film, or bigger digital sensors, record more fine detail. This is why two cameras both having 8 mega-pixels may be far apart in quality terms - the digi-cam with its small sensor has far less resolving power than the SLR with a large, high quality sensor.
The ISO of your system is also important. With film, the smaller grain allows for recording of finer detail, and with digital, less noise is created at lower ISOs. Always use the lowest ISO possible.
Finally, the quality of your lenses is of course very important, but less important than the elements mentioned so far. Buying a better lens will not help you take sharper, more richly detailed images unless you address all of the above points first.
How you deal with your image in Photoshop can effect the quality of your image. Poor Photoshop technique can very quickly ruin fine detail - poor retouching, not understanding the image size dialog box, and bad sharpening can all be catastrophic to an image's fine detail.
final factor, of least but still significant importance, is the
printing system's ability to resolve detail and it's native resolution
(PPI). This is where 300 PPI comes into play. Of course, 300 PPI of
unsharp, out of focus data will result in an unsharp, out of focus
print with no detail. But if you've managed the process properly up
until the point of printing, then the ideal situation is to send the
data to the printer with no further scaling by the printer's driver or
Here are some popular printers and their native resolutions:
Beyond these resolutions there is very little increase in resolved detail. As a good default, 300PPI is a sensible figure to use if you don't know the resolution of your printing system, and in general will result in very high quality results assuming good quality pixels.
In many ways, it is best to flip this discussion on its head and ask - how large can I print the files I have? Assuming you have shot a truly sharp image using good technique and high quality systems, then depending on your capture system, you will get a truly sharp print using the following formulas:
The lower number you divide by, the less pixels you need to make a sharp print. This is because the quality of those pixels is higher in those systems - more of those pixels are being used to actually record detail, and less to record noise/grain etc.
There is in fact much more to the story of resolution, detail and sharpness, but these are the basics. Master these are you will be well on your way to sharp, richly detailed prints.