There are two reasons why your pictures might not get stitched correctly: a wrong setting of the entrance pupil and maybe even more optical distortions of your lens or zoom lens. This is due to the shape of your lens, the aspheric lens. Here is how to know or correct it...
Here is really the more important edit to realize, before stitching the photos, when it's really necessary. Indeed, optical distortions of pictures are often so important that panorama software have a hard time to stitch together two consecutive pictures even for the best of them like Autopano Giga (even the last version 2.6 considerably improves the problem) and PTGui. And even if the camera was well placed at the entrance pupil.
Caution!when a panorama is badly stitched so the lines are distorted, it's impossible to know a priori if it's a problem due to complex distortions that the panorama software can't correct or a parallax problem hence a wrong placement of the camera at the entrance pupil. You know it's a problem of distortions if you're sure of the setting of the entrance pupil. But currently, these two types of defects don't look alike.
Even if certain pieces of software can very well correct a classic distortion, barrel distortion most of the time and even quite pronounced, numerous lenses are unfortunately cursed with distortions called "moustache distortion" or even "cop hat" which are really hard to correct and put numerous pieces of panorama software on their knees. So here are a few leads...
If you're a beginner...
A new part of this guide is now dedicated to you. You'll find simple pieces of advice to implement to stitch nice panoramas, choose your software, your equipment...
Since the release of the new version of Autopano Giga and Autopano Pro 2.6, one of the major news in my opinion is the introduction in stitching algorithms of a correction of complex distortions often cursing lenses like short focal lenses. IT IS NOW POSSIBLE TO STITCH THE GREAT MAJORITY OF SHORT FOCALS ALMOST PERFECTLY.
Certain lenses that were impossible to stitch like 14 mm can now be stitched more than correctly, even perfectly. A few Photoshop edits remain but there's no possible comparison with the previous versions and other stitching pieces of software. Some other lenses, zoom lenses, short focals that were stitched just correctly can now be stitched perfectly. Almost a miracle! In order to give credit where credit is due, you want to acknowledge that PTGui managed already to make this small miracle...
Optical distortions?
Certain wide-angle lenses distort the edges of the image in a shape of "pincushion", "barrel" or even "moustache". So the edges of the images are either curved outwards in barrel (1), either inwards in pincushion (2), or a bit of each in moustache (3) as shown in the pictures below.
This is due to the shape of the first lens. When it's really rounded, there are risks for the image to be in barrel, when it's convex, to be in pincushion (which is more unusual) and when it's aspheric, the image will show "moustaches" distortions. This is obviously a more and more common issue as manufacturers introduce more and more aspheric lenses - it's easier today to manufacture in big quantities - in their optical formulas in order to improve the quality of the images from the center to the edges of the photos. In this way, in two consecutive pictures, the optical error will be opposite. It's impossible for a photo panorama software to combine these two photos without a previous correction of this distortion because only two spots - at the junctions - are superimposed.
Example with barrel lenses.
In the best case, some stitching pieces of software take it into account and this is why they come with a database on every digital camera on the market - including of course regular updates to take newcomers into account! -. Before stitching the images, the software will thus ask you with what camera the pictures were taken, unless it detects it automatically by reading the Exif data of the files.
In the case of numerous lenses, the distortions are really very important and it's essential to take them into account during the stitching process. With these lenses, when the photos stitch poorly and unlike one could think, it won't necessarily be a parallax problem hence of entrance pupil or nodal point but really of distortions. In most other cases, these distortions must absolutely be corrected before opening the pictures in the panorama software... whenever possible! There are few cases when, even a bit distorted, the images are stitched correctly because their distortion is "sane" hence simple.
Note
As an example, I'll take a case I've experienced with the lenses of the Olympus E1, E5, 500 or 330 and Autopano Pro 1.42. That's when I became aware of the problem and found solutions. Let's take the two wide-angle lenses I had: the 14-54mm and the 11-22 mm at 14 mm (thus equivalent to 28 mm).
With the 14-54 mm zoom lens at 14mm, the moustache distortion were so important that Autopano Pro alone was unable to correct them. The stitching was of poor quality.
With the 11-22 mm zoom lens at 14 mm, the barrel distortions were still there, but they were simple (without moustache) and Autopano Pro could correct them very well and realize a very good stitching.
Correction of optical distortions
For several years I tried any tool allowing to correct optical distortions before stitching. I was never satisfied: DXO, PTLens,... and when Photoshop CS5 was released I had a nice surprise: Lens Correction.
Lens correction from Camera Raw 6.1 and next...
Since the CS5 version of Photoshop and 3 of Lightroom, Camera Raw or the module of development come with a new correction tool of the main lenses defects: vignetting, chromaticism and above all distortions. All of this is part of the workflow in Raw which is a godsend! The sixth tab " Lens corrections " (1) is thus now doubled: the former tab of manual correction and this new tab "Profile" (2) gathering the registered profiles in a database. This base doesn't have all the lenses on the market yet, even though it already has lots but when it's the case, it's very efficient... To know it, you only have to click the button "Activate profile corrections of the lens" (3). If the lens is in the database, the data will appear automatically in the Lens profile (4).
Finally, I'd like to say! My first impressions are very positive. A lens that was poorly stitched now developed in Camera Raw with this option activated and stitched in Autopano Giga 2.5 often gives startling results. So here is a piece of advice: try it!
Note! with Autopano Giga 2.6 or PTGui, it's not even always necessary so you should try with or without correction of the distortions to get a proper idea...
Fun fact!
I worked for a long time with this Canon 17-40mm lens. There were many advantages and one big drawback. This lens was one of the first Canon lenses to benefit from the new anti-reflective coating from the last lens (towards the sensor), so important in digital photography because digital sensors are way more reflective than films and thus subjects to flare. Secondly, it allowed me to work with two focals I like: the 17 mm and above all, when I'm trying to realize panoramas by stitching, the 35mm. Yet this lens has a big disadvantage: it comes with aspheric lenses creating moustache image distortions! For a long time, I tried different kinds of software such as DXO or PTLens to correct the distortions BEFORE stitching but that was of no use. With Lens Correction it works! I changed lens ever since but when I'm trying to stitch old photos, I don't have the issues I was facing some time ago. And once again, since Autopano Giga version 2.6 was released, the problem has disappeared. So much progress in so little time... for other software it's not quite it, except for PTGui!
About efficiency of distortions correction software...
It's impossible to know beforehand if PTLens or another distortions correction software will or will not be efficient to edit your lens' distortions. If you get the impression - though real! - to the naked eye that the software is straightening out fine all straight lines from one photo, you notice that the efficiency of this correction, once the photo stitched, is often close to non-existent. This remark is even more accurate if you shot a geometric subject or an interior.
Most of the time indeed, the straightening is only performed to line up the items on one single line or to straighten slightly curved lines. But homothety of the distances on this now corrected straight line isn't respected. The stitching is of poor quality because too complicated to edit in Photoshop hence useless.
There are cases when correction is formidable - even essential - and works perfectly and others when nothing ever comes out of it. To make a high-def, quality stitching, you're thus only left with the option to change lens or spend lots of time on Photoshop.
A few examples...
Here are a few examples of pairs digital camera / lens / correction software and what I could note:
Hasselblad H3D 31 / 28 mm / Phocus: Corrections possible in the dedicated Phocus software but uninteresting when it comes to the quality of the panoramic stitching. Perfect stitching in APG 2.6 but manual addition of checkpoints compulsory. Nikon D7100 or D300 / 16-85mm DX Nikkor at 16 mm / DXO: Corrections possible but uninteresting. Poor stitching as well. Nikon D90 / D7100 or D300 / 10,5 mm DX Nikkor FE: Almost perfect stitching without correction of distortions. Canon 70D / 8,5 mm Sigma FE: OK stitching without correction. Canon 5D / 15mm FE Sigma: OK stitching, not more. Canon 5 D Mark III / 15 mm Canon FE: Very good stitching, even almost perfect, without distortion correction. Nikon D7200 / D300 / 17-55mm2,8 DX at 17 mm: OK stitching without correction. Canon 1 DS Mark III / Canon 35 mm F1,4: very good stitching with Lens Correction from Camera Raw correction. Nikon D810 / 35mmF1,4 Nikkor AFS: Very good stitching but only if you manually set checkpoints for interior shots.
In the next page, we'll see what are the basic principles of the method by stitching because stitching is studied in details on the pages dedicated to Autopano Giga - Panoramic stitching
"Find the nodal point or no parallax point accurately in less than an hour"... whether you are photographing a simple panorama or a 360° photo - PDF of 100 pages -More information...
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Caution!
Note 
As an example, I'll take a case I've experienced with the lenses of the Olympus E1, E5, 500 or 330 and Autopano Pro 1.42. That's when I became aware of the problem and found solutions. Let's take the two wide-angle lenses I had: the 14-54mm and the 11-22 mm at 14 mm (thus equivalent to 28 mm).
Since the CS5 version of Photoshop and 3 of Lightroom, Camera Raw or the module of development come with a new correction tool of the main lenses defects: vignetting, chromaticism and above all distortions. All of this is part of the workflow in Raw which is a godsend! The sixth tab " 
I worked for a long time with this Canon 17-40mm lens. There were many advantages and one big drawback. This lens was one of the first Canon lenses to benefit from the new anti-reflective coating from the last lens (towards the sensor), so important in digital photography because digital sensors are way more reflective than films and thus subjects to flare. Secondly, it allowed me to work with two focals I like: the 17 mm and above all, when I'm trying to realize panoramas by stitching, the 35mm. Yet this lens has a big disadvantage: it comes with aspheric lenses creating moustache image distortions! For a long time, I tried different kinds of software such as DXO or PTLens to correct the distortions BEFORE stitching but that was of no use. With 
Hasselblad H3D 31 / 28 mm / Phocus: Corrections possible in the dedicated Phocus software but uninteresting when it comes to the quality of the panoramic stitching. 
