Does evolution only give rise to traits that confer fitness? In other words, does the existence of a trait imply it's conferring of fitness? If not, what are some counter examples?
Rephrasing the question
Does evolution only give rise to traits that confer fitness?
The phrasing is actually a little nonsensical, but it is easy to understand what you mean. The reason is that "fitness" is not a characteristic of individuals but a measure (a variable if you wish) of a characteristic. Imagine you are talking about Shaquille O'Neal and you say "He is height!" instead of "He is tall!". Allow me to rephrase the question correctly. Note that because "high fitness" is a statement relative to the fitness of the others (just like being tall is relative to the average height), I highlighted in my rephrasing of the question this relativity.
Does evolution only give rise to trait variants that are associated with higher fitness than other variants?
Very simple examples include all the genetic diseases.
In short, evolution is much more than natural selection. All of the following are reasons for why there are low fitness variants in nature.
- genetic drift (incl. bottleneck or founder effect),
- spatial variation in the environment and gene flow (hence migration load)
- changing environment (incl. the biotic environment and the social environment) and non-equilibrium conditions in general
- local peaks in fitness (and the concept of pseudo-species; fitness landscape)
- genomic conflicts
and many others...
For more information on the "why" part of the question, you should start with an intro course to evolutionary biology such as Understanding Evolution by UC Berkeley for example.
I'll try to beat @Remi.b to the suggestion that you review Understanding Evolution as a general overview of evolutionary topics.
For a quick answer: no.
Sometimes people confuse the great importance of natural selection in evolution with an equivalency between natural selection and evolution. However, there are many many contributors to evolution, many of which do not involve fitness.
I'll list just a couple examples:
Genetic drift is random change in allele frequency because of random sampling of reproductive organisms.
Founder effect is a somewhat related concept, referring to the change in allele frequency in a population that becomes isolated from the rest of the individuals of a species: that population has a selection of traits that might differ from the species as a whole, and lead to future speciation.
There are many more.