There are several problems which can occur if a Newtonian is no collimated properly, some of which are more detrimental to the image than others. The following drawings show several common ones.
If the focuser and secondary are both about right, but the primary is tilted then the image that is reflected back to the secondary from the star will not be coming from the axis of the mirror's parabola. This causes coma which is a blooming of the star image. The stars in the eyepiece will not come to a focus no matter how many times you focus. The faster your system, the more severe this problem. This is easy to correct by adjusting the screws on the back of the primary's mirror cell. Primary tilt is shown below:
The drawing below shows the secondary tilted wrong so that the light does not enter the eyepiece parallel to the optical axis of the eyepiece. This usually causes astigmatism which shows as the star is de-focused. The star will appear to be a line, then it will make a line perpendicular to this as it is focused from inside to outside focus. The system shown below should have the secondary's tilt corrected so that the reflected optical axis of the primary is both parallel and centered on the eyepiece.
Sometimes the system is collimated and the optical axis of the primary is coincident with that of the eyepiece, but the secondary is simply in the wrong position. Since the secondary is flat it has no optical center like the primary and eyepiece do. It works just as well off center. The only problem is that it will not reflect all the light from the primary and the images will be darker. Stars will come to a focus, but they will not be as bright as they could be because some of the primary's precious light is being thrown away. This secondary (shown below) needs to be moved forward and up in the tube. The spider may not be centered in the tube. Remember that with fast telescopes that there should be a small amount of offset such that the secondary is a little further from the eyepiece that the opposite side of the tube. This problem is certainly less severe than having optics tilted as they are above.
Another problem that is less common, but does come up is having the secondary off center. If the telescope is collimated with the mirror in this position it will give good images, but the optical axis will not be parallel to the physical one. The telescope tube could vignette the light entering the front of the instrument. Also this can make using setting circles a problem. This is shown below:
Having the focuser not square to the tube won't necessarily be a problem if the secondary is also tilted. This is not recommended, but if the focuser can't be perfectly square due to an uneven tube, then as long as the secondary is tilted so that the paper ring is under the Cheshire cross-hairs and the primary is collimated as normal, the telescope will still give good images. Most secondary holders are designed to be mounted at a 45° angle. Because of this they will block extra light that should be hitting the primary if they are set to some other angle. Usually the amount of tilt is so small that it causes no problem. This is shown below:
