How to determine what size telescope to buy A couple of years ago my son showed an interest in astronomy and we bought a 6" reflector telescope.  We use it pretty regularly and have enjoyed it immensely.  Lately we've both been wishing we had something bigger to be able see more things and to see what we can see now with more detail.
How do you determine the size of telescope needed to view a certain object?  
I understand that there are a lot of other factors that come into play when talking about what you can see and how well you can see it. Ideally I suppose what I'm looking for is some sort of chart/table that gives a general guideline of the scope size and some of the objects that should be viewable (with an average setup).  
Are there any such resources?
 A: Geoff's answer is relevant. A few more things to add:
There are two things that a bigger aperture will provide: more resolution, and more brightness.
In terms of resolution, things go downhill pretty fast after 150 mm (6"). You'd think a 300 mm (12") aperture scope would provide 2x more resolving power, but in reality it's not that simple. There's something called "seeing", which is the stillness of the air that allows you crisp sharp views, and it varies a lot with the place and time. Realistically, instruments bigger than yours (which has about 0.7 arcsec resolving power) will use their resolving power much less often, only during those fleeting moments of perfect seeing. The bigger the scope, the less often you're able to use its full resolving power, because atmosphere is turbulent and keeps churning all the time.
E.g., a 100 mm (4") instrument will provide 1 arcsec resolving power. How often you'll get 1 arcsec seeing, or better, in the place you live? Not very often, unless you live in California, or Hawaii, or some other place with excellent seeing, far from the jet stream. People living in the american north-east often find that instruments bigger than 4...6" are seeing-limited a lot.
Related to resolution, an alternative way to look at it - magnifications up to 100...150x are basically almost always usable. Around 200x, depends on seeing. Over 300x become less often achievable. Beyond that, it's pretty rare that you could crank up the mags without getting a large blurry blob instead of a crisp image.
Now, the second issue, brightness. A 300 mm scope will capture 4x more light than your 150 mm. So it would allow you to see fainter objects. But remember, if you live in the city, there's something called light pollution, due to all the lights around you, that makes the sky glow with light, so the faint objects are hard to see. You'd have to drive an hour or two to the dark skies away from the city to see all the really faint fuzzies. If you own a huge 24" dob then you could only exploit all its light-gathering power in those rare places with zero light pollution.
So, realistically, there are limits to what a big scope could do. Many old experienced users say that a 300 mm (12") f/5 truss dobsonian is the biggest that can be used without major effort. If it's a tube design, instead of truss, then it must be even smaller. Opinions about the real limit will vary between 10" and 16", with most of these scopes being f/4 to f/5.
It's best if you could go to a star party and test a few different scopes yourself.
In any case, the 6" will last you a long time and it's a quite capable instrument. Enjoy.
A: There are lots of mathematical answers to this question, but I'd like to make a few qualitative observations instead, based on 54 years using telescopes of all kinds and sizes, from 40mm refractors to 74-inch reflectors.


*

*Unless you have some specialized purpose, don't consider anything
smaller than 6 inches aperture. Small telescopes look cute, but don't
show you much, especially if you're a beginner. Experienced observers
can tease amazing observations out of tiny scopes, but most of us
will be happier to give these a pass. Aperture wins.

*A 10-inch Newtonian on a Dobsonian mount is something of a "sweet
spot." It's about the smallest aperture to show significant detail in
deep sky objects, yet is compact and light enough to be easily
transported to dark sky sites.

*Above 10-inches, the more aperture the better, provided you can
comfortably transport, set up, and operate it. This is crucial! The
nicest telescope in the world is useless if it never gets used. I
find even a 12-inch Dob becomes bulky, cumbersome, and heavy.
Aperture wins, but only if you use it.

A: I think what you are looking for is the aperture magnitude relationship.
Your current reflector has an aperture of 6". The more aperture you have the fainter the objects you will be able to see. 
Fainter objects in the sky have a higher magnitude.
Celestron has table on their website (reproduced below) along with a full explanation of the math used to get the numbers:
Aperture       Magnitude limit
3.1" (80mm)    12.2 
4"   (100mm)   12.7 
5"   (125mm)   13.2 
6"   (150mm)   13.6 
8"   (200mm)   14.2  
10"  (250mm)   14.7  
12.5"(320mm)   15.2  
14"  (355mm)   15.4  
16"  (400mm)   15.7  
20"  (500mm)   16.2

Keep in mind that the numbers above are for ideal viewing conditions. 
A bigger scope will also give you much brighter and clearer views, here's a comparison from obsession telescopes.

