Is there a standard quality ranking for oil paints?
How do specific oils relate to the quality of oil paints?
Can anyone provide a top five or top ten of brands?
As mentioned in the comments, an absolute ranking of brands would be primarily opinion-based, as there are as many preferences and requirements of oil paints as there are artists.
However, a lot can be said about the quality of oil paints, and the range is sufficiently large to allow for a general objective positioning of brands within that spectrum.
Oil paints are suspensions of pigments in oil, sometimes in conjunction with small amounts of other ingredients - fillers, waxes, resins - that change their characteristics.
Both oil and pigment have vastly varying differences in quality, and, together with their ratio, determine the level of quality of the paint.
Higher lightfastness of both the oil and the pigment, and higher opacity and colour retention of the pigments, are the characteristics of an oil paint of good quality. In addition, the artist will generally need less higher quality paint to acquire a same amount of colour luminance.
The type and purity of the oil influences the drying time, the clarity of the colours, and the lightfastness of the paint.
Linseed oil is the most common oil used in manufactured paints. Poppy oil is sometimes used as a replacement: it is more expensive, but also more lightfast and transparent.
The quality of the pigment - its particle size, origin, and purity - are important for the quality of the paint: they are decisive for the permanence, brilliance, and stability of the colour. A higher ratio of pigment, referred to as pigmentation, will increase the opacity and intensity of the paint, although making the paint relatively thicker and faster-drying. Especially in lower ranking oil paints, pigments are often replaced by chemical alternatives - although in some cases they have achieved better painting characteristics than their antecedents, or even surpassed them.
A famous example of a high quality pigment that is almost always replaced by a synthetic substitute is ultramarine: traditionally, this is made from the semi-precious gemstone lapis lazuli (found 'across the sea' from Italy, or 'ultra marina') that is ground very finely. Hence, the oil paints containing it are expensive.
Other substances may be added to the paint to change its properties, like drying-time, UV-resistance, and glossiness. See here for an overview.
On the other hand, in economy paints, fillers may be used that improve the consistency of the paint, while suppressing the costs.
Keeping the above information in mind, the vast differences in quality of oil paints are obvious. With that knowledge, looking through the information on their websites will allow you to decide what you are willing to pay for what level of quality, based on your personal preferences and style.
Some brands (like Winsor & Newton) offer multiple series in multiple ranges, whereas other names (like Old Holland), are exclusively producing paints of a specific level.
At the top of highly qualitative oil paints, brands like Old Holland, Holbein, Schmincke Mussini, Sennelier, Blockx, Michael Harding, and Williamsburg, all of which are at least more than a century old (excepting the last one), have established an excellent reputation among professionals.
Mid-range we find brands like Gamblin, and some of the Winsor & Newton series.
At economy level, Royal Talens' Rembrandt, Winsor & Newton's Winton, Royal Talens' Van Gogh, and Grumbacher have been helping out students and hobbyists around the world.
Generally speaking, the higher the price, the higher the quality. The generality of this rule is more applicable here in the field of (oil) paints, than in many other. Do note that this only really applies to well-established brands as sold in respectable art stores.
There is no standard quality ranking for artist oil paints, however, generally, they are sold as Professional, Artist or Student grade with different brands having their own names. Price also is usually an indicator.
I think it is more useful to think of paint in terms of purity rather than quality.
The top end manufacturers are pigment makers firstly, the rarer the material and the more complex the manufacturing process the more expensive the pigment and thus the paint. (See Lapis lazuli, rose madder, mummy brown for examples). The most expensive paint contains one expensive pigment with oil added. A cheaper paint in the same range will be exactly the same quality only with a pigment that is easier to produce.
Budget paints will have two or more cheap pigments (and possibly filler) mixed together to resemble a single pigment.
The oil is basically a medium to get the pigment from the tube to the canvas, cure, harden and then leave the pigments in as pure a condition as possible. Different oils are used, the most common is heat-treated linseed, I have also used walnut oil and safflower oil. The different oils have different effects on drying time, consistency, and finish, but this is a good thing as it provides flexibility and creativity which in my opinion is the essence of oil painting.
I have read that safflower oil separates in the tube and that linseed oil goes hard over time. I would say that that is just a common problem that relates to ageing or poor storage.
You can find a list of popular brands looking online, if you are a student you could start with something like Monte Mart, Maries, or if you had a bit more money to spend you could look at the Winsor and Newton Winton range.
If you are serious and want to keep going you will probably be able to answer your own question by that time and discover brands like: Blockx, Michael Harding, M.Graham, Sennelier... I use M.Graham and Art Spectrum.
Though there may be no definite answer other than your own experimentation, consider the pigment composition. Check a tube of oil paint and note how many different pigments are included; as a coarse rule of thumbs, the lesser the better.
Also light fasting (how fast the paint will fade over time) plays an important role.