Reproduction
Various reproduction methods for the Transformers species have been demonstrated across various continuities.
Mechanical construction
Sometimes new transformers are simply built from scratch and that's all it takes. A suitable transformer body is constructed and when finished and turned on it just springs to life. Two notable examples of this type of reproduction appear in the Generation 1 cartoon when Wheeljack and co. created the Dinobots, and later when the temporarily super-intelligent Grimlock created the Technobots.
The Dinobots were initially very simple mentally, and were ordered to be deactivated because they were too dangerous. Wheeljack then developed a set of crown-like devices to place on the Dinobots which greatly enhanced their intellect, although they were still "dumb" and child-like compared to the other Autobots. The Technobots, on the other hand, were immediately fully-functional and some of them were even smarter than average Transformers. If one were to take these facts as canonically meaningful (rather than simply the whims of the writers of those episodes), it could be guessed that programming a functional Transformer brain from scratch is extremely difficult, such that even Wheeljack was not up to the job. Temporarily super-genius Grimlock may have been the only one capable.
At least on the surface, this "built from scratch" approach runs counter to claims in other episodes of the show that Vector Sigma is needed to create new Transformer life. (See below.) However, since Vector Sigma is presented as being a supercomputer, and not a "magical" device like the comics' Creation Matrix, it could fall into line with the speculative statements above regarding Grimlock and Wheeljack. Perhaps Vector Sigma is simply an advanced enough computer that it is capable of constructing a working mind. The Infusion method below may have been possible in The Technobot's case if Grimlock could scavenge enough energon from Unciron's remains, but this seems more unlikely with the Dinobot's creation with the relatively Energon low Ark.
Infusion
In other stories, once a new Transformer body has been built it must still be infused with life (what the fiction from the Beast era and after would gloss as a spark) from a powerful "god-like" outside source. In the Generation 1 cartoon this source was Vector Sigma; in the Marvel comics it was the Creation Matrix, which housed the essence of Primus, the Transformers' creator-god. In the Beast Era cartoons, sparks arrived from the Allspark, perhaps through Vector Sigma. In the Marvel comic and Beast Era cartoons, each Transformers' life-force was a fragment of Primus' own.
In the Young Corgi book Desert of Danger Hot Rod refers to his creation after the Ark left Cybertron as when he was "matrixed". How exactly this would have happened if Optimus Prime was aboard the Ark with the Matrix at the time is unknown, but one option might be the Matrix Flame.
The Matrix flame was an artifact which allowed Transformers on Cybertron to access the power of the Matrix even when it was no longer on Cybertron. Literally a flame, it was used to breath life in the super warrior Ultra Magnus The flame was somehow linked to the Matrix, and when the Matrix was transported to another dimension during Target: 2006 the flame went out, forcing the Autobots on Cybertron to investigate.
The Dreamwave More than Meets the Eye Guide provides yet another method of infusion.
According to the guide, in Dreamwave continuity Transformers generally begin life as a skeletal mass of partially formed circuits: a Protoform. These are kept in stasis pods filled with nuturing nutrient gell. They can be built to specific specifications or be fairly general, allowing the robot to form naturally upon introduction of a spark. Sparks, and hence life, usually come from the Matrix, *BUT* if the Matrix is absent life can be granted by attuning the protoform to an energy wavelength similar to the Matrix and then applying a concentrated burst of energon. This is rarely used as it is extremely resource consumptive requiring restrictively high amounts of energon.
The live action movie continuities function along these lines as well, with the Allspark being the source of infusion.
Resurrection
Though not quite the same as reproduction, a copy of the mind or essence of a previously living Transformer may be introduced into a new body and through some vague process return that Transformer to life. This occurred when Starscream created the Combaticons in the G1 cartoon, and in the comic when Prime used copies of the minds of existing Cybertronians to create the second series Autobot cars on Earth. Another example from the comic occurs when Optimus Prime himself is returned to life merely by inputting a human's floppy disk copy of his mind into a new body.
In his ending to the Beast Wars: Transmetal video game Ravage uses "a prototype cloning device based on transreplication technology" to clone the deactivated G1 Decepticons on the Ark into new protoform bodies.
This is included as a means of reproduction because it seems likely from the dialogue that the Autobot cars created via copied minds by Prime on Earth still existed on Cybertron when he left, meaning that if they survived, two of each of these individuals now existed.
In the Unicron Trilogy story "Linkage", Redline and Falcia combine energy from their spark frames in order to create a new body for the mind/soul of Twirl to inhabit after her Mini-Con storage panel was destroyed in battle. This led to an interesting relationship between Twirl and Falcia (see "Familial relationships" below).
Budding
The Transformers: Generation 2 comic introduced the concept of asexual "budding." Bubbles and lesions of apparently liquid metal formed on a robot's chest accompanied by energy discharge, the process grew more intense until the point where a large mass of liquid-metal burst free from the chest and slowly formed, first into a protoform-like blank figure, and then solidified into a full Transformer. Illustrations suggest that this was something of a communal event, with others surrounding the budding robot in a circle.
It was revealed that (in the Marvel continuity at least) early Transformers reproduced this way until they reached the population level Primus desired. At this turning point, the practice stopped and all memory of it was erased. When the Cybertronian Empire (possibly under influence of the Leige Maximo) rediscovered and revived the process sometime during the 4 million years after the Ark's loss, the successive generations of robots produced were increasingly less sentient and emotional (as Primus's lifeforce was apparently spred thinner and thinner between them) and the lifeform called The Swarm was created as a byproduct.
Sexual reproduction ???
Despite most continuities having male and female genders (gender being a mental and social classification as opposed to "sexes", a physical distinction) and a definite, strong history of romance existing between these genders, there is little canonical evidence for Transformers reproducing sexually. (Though admittedly there isn't a lot of direct evidence for humans reproducing sexually in most Transformers media, which is, after all, aimed towards kids.)
In the Generation 1 cartoon the male Transformer - Female Transformers romance could perhaps be explained as an artifact of Quintesson mental programming very closely echoing the organic life forms the Transformers were built to serve.
The best case for sexual reproduction in the species could probably be made from Beast Wars, where Rattrap makes numerous off-color remarks throughout the series, especially directed at Silverbolt and Blackarachnia. These comments strongly hint at something sex-like among Transformers, though it could of course be merely recreational rather than reproductive.
Airazor and Tigatron's fusion into Tigerhawk durring Beast Wars could perhaps be seen as example of sex-like reproduction (two beings comming together and creating a new being that is a recombination of their components) Though it could also just be glossed as an extension of the usual Combiner-team type merger.
It is unknown what effect the Beast Machines reformatting of Transformers into technorganic beings that are equal part organic life and mechanical to a cellular level has on their reproductive options. It is concievable but unexplored whether this new form of Transformer life could reproduce sexually.
It should be noted that during a dream-like vision, Blackarachnia and Silverbolt met in an ethereal state, and the two appeared to "merge" their sparks, which may be as close to sexual intercourse as Transformers get (perhaps a more spiritual act than physical).
Familial relationships
One confusing aspect of this apparent lack of sexual reproduction is the canonical use of genealogical terminology to describe certain relationships. The most common of these is when two transformers regard each other as "brothers" (e.g. G1 Sideswipe and Sunstreaker, or RID's Optimus Prime and Ultra Magnus) or "sisters" (Roulette and Shadow Striker).
Again, the Dreamwave More than Meets the Eye Guide provides a partial possible answer. According to the guide when a spark naturally splits as it's being introduced to a protoform, it creates two robots who are "Brothers" such as Sideswipe and Sunstreaker. When such a spark division is artificially induced, the less balanced and self-reliant pair created are refered to as "Clones." (This definition of "Brother" may or may not apply to RID Prime and Magnus, whose brotherhood was said to result from the special circumstance of having been created simultaneously by Alpha Trion).
However, the "Beast Era" widened the issue of reproduction with Rattrap referring to his "great-aunt" Arcee and in general the practice of Maximals and Predacons referring to the Autobots and Decepticons as their respective "ancestors", as well as themselves as being their "descendents", implying a direct genetic (for want of a better term) lineage. Various sources of debatable canonicity suggest that Optimus Primal is specifically descended from Optimus Prime, usually through the phrase "his ancestor Optimus Prime". The aforementioned Mini-Con Twirl very specifically calls Falcia her "mother" (which Falcia hates) and seems to treat Redline like a father, since the two's spark frame energy went into constructing her physical form. In the Armada cartoon, Side Swipe refers to Hot Shot as his brother after Hot Shot saves his life, indicating at least an understanding of the concept.
In the absence of sexual reproduction, the use and meaning of these genealogical references is difficult to explain. One possible example - as show in the Beast Era - is when Airazor is brought to life. Her spark and protoform is heavily damaged, and Cheetor allows his spare parts while Rhinox guides the proceedure. To compare to humans, this is something like assisting with childbirth and donating blood or organs. It is unlikely that this happened enough to cause 'descendants' as they are shown, however.
Toys
In the real life continuity, when two toy manufacturing companies love each other very much, one of them may start shooting Transformer design propositions to the other one. There, during several months of gestation, engineers will work on those designs, which will be developed into functional and manufacturable Transformers. Once the Transformers are ready to be produced, the design will be sent to marketing, and ultimately to the chain manufacturer for the delivery. Voilà! A new Transformer is born!
