New Ability

Symbiotes feed on their host's adrenaline, usually released into the bloodstream during the fight-or-flight response. They have also been shown to depend on their hosts for a steady supply of phenethylamine, a chemical found as a neurotransmitter in the human brain. While this has been known to lead some symbiotes to consume the brains of others, the chemical can also be ready found in processed chocolate. While the symbiotes are connected to a host, they raise their host's dopamine levels. They can apparently be killed, or at least forced into some sort of death-like state, by an overdose of dopamine-inhibitor. Symbiotes aren't able to bond with hosts who have high levels of vitamin C in their blood streams. There are several levels of biological symbiosis, or "bonding" that can be achieved between a symbiote and its host, each with different biological consequences.
Symbiotes have some ability to sense the thoughts and emotions of sentient creatures, though to what extent remains unclear. The Venom symbiote was able to pattern itself after Spider-Man's thought, and respond to his mental commands even without significant bonding. The psychic scream of the Venom symbiote was able to draw the attention of space-faring symbiotes, while powerful feelings of emotional anguish were able to actually kill many symbiotes.

Symbiotes have a genetic memory, allowing them to exploit their parents' knowledge through ancestral recall. On Earth, this allows Venom's descendants to benefit from the symbiote's former bond with Spider-Man by gaining spider-like powers. Certain memories seem to be more readily accessible than others. For example, the trauma of Galactus devouring a word populated by symbiotes so scarred the surviving members of the species that it still invokes an intense reaction in all symbiotes today.

Symbiotes are genderless, reproduce asexually, and generally produce only one offspring in a lifetime. In the case of Venom, seeds were forcibly extracted to produce more offspring. There is no family structure, and in fact it seems to be common for parent and offspring to hate each other. However this observation is taken mostly from the relationship between Venom and his children. Venom hates Carnage because of his murderous nature (not to mention that when they were cell mates they had an antagonistic relationship). When his other "children" were born he thought that they would end up like Carnage so he placed his hatred of him on them. However, recently the Venom symbiote was pregnant after absorbing a clone of itself and wanted to rebounded with Spider-Man because bounding with Brock would kill the child because he had cancer. While they have a latent ability to sense the proximity of their progeny, they usually have no interest in them. The one exception comes once every 1,000 generations, when a symbiote is born with a high risk of psychotic breakdown, and must be guided by older symbiotes, or else destroyed.

Their unique properties make the symbiotes immune to most conventional weapons. They are dense enough to absorbed the force of powerful blows and stop bullets before they reach the host being. They are able to process breathable gases for the host when it would otherwise be unable (underwater, for example). They seem to confer a weak healing factor on strongly-bonded hosts, but that bond can also send host and symbiote alike into shock if they are forcibly separated.

Symbiotes seem to have some latent psychic abilities, allowing them to respond to the thoughts of their hosts, and each other. When Venom's symbiote was in anguish, it let out a psychic scream that effected sensitive humans worldwide, and was received by symbiotes in a nearby star system.
The symbiote amplifies the strength of its "wearer", so that a reasonably fit human (such as Brock) can compete and even exceed even Spider-Man's strength. It also confers improved speed and agility on the host.
By virtue of having partially bonded with Spider-Man, Venom and its descendants all have spider-like powers, including the ability to cling to surfaces and produce organic webbing. Most can also avoid detection by Spider-Man's "spider sense" might also work on other people such as electro in web of shadows.
Abilities
Symbiotes can control the actions of their hosts at a certain point.
Symbiotes that have fully bonded with their hosts have a more biologically complex symbiosis with their hosts, and can share thoughts and memories with them. Carnage has also been known to hide in its host's blood stream.
The symbiotes are said to have 'genetic memory,' and can read the memories of others of their kind by absorbing chunks of their material.
Symbiotes tend to be dense, and can absorb even the force of bullets before they reach their hosts.
All symbiotes have the ability to form tendril-like psuedopods. Venom has used this to great effect by forming weak tendrils and shields from his constituent matter. Carnage discharges tendrils of his constituent matter instead of webbing. Scream has numerous tendrils composing her costume's "hair", which she has used as a powerful whip.
Terrestrial symbiotes additionally have the power to form solid appendages from their bodies, and have been shown to form spikes, talons, and blades. Carnage was known to throw axes from time to time, but the weapons quickly crumbled when separated from the symbiote. Venom's ability to form webbing is probably a primitive form of this ability. Mac Gargan has been shown to be able to form a scorpion-like tail while hosting the symbiote, and the Venom symbiote of Earth-982 allowed host Norman Osborn to form solid appendages, such as a extra limbs. This shows that any symbiote can gain the ability to form more solid appendages if exposed to the Earth environment for a long enough period of time.
The Life Foundation symbiotes have also been shown to form a powerful acid from their constituent matter. The Venom symbiote of Earth-928 in the year 2099 demonstrated an ability reduce an engulfed victim to bones within seconds, using the ability to kill New York gang leader Bloodmace. This may suggest that any symbiote exposed to the Earth environment for a long enough time may gain similar powers.
Venom and his descendant symbiotes have been shown to be adept at controlling their coloration. This allows them to take on the appearance of normal clothing, to provide highly effective and complex camouflage, and to even disguise their hosts' physical features.
Symbiotes have the ability to process breathable gases when the host normally cannot breathe (for example, in water).
Symbiotes can expand to any limit in order to cover any host or object.
Symbiotes seem to have some ability to combine their constituent matter. During Maximum Carnage, the Venom and Carnage symbiotes seemed to mix in an attempt to destroy each other. Later, the Carnage symbiote would absorb other symbiotes during the symbiote invasion of New York. The Venom symbiote recently absorbed a cloned symbiote worn by Patricia Robertson. The Hybrid symbiote is the merger of four of the Life Foundation symbiotes.
There is evidence to suggest that the relative power - or at least physical strength when bonded to a host of comparable build and musculature - increases with each generation, given that Toxin is known to be much stronger than his "father", Carnage, who in turn is known to be significantly more powerful than his progenitor, Venom.
It was revealed that the window period between the contact and the full bonding between a symbiote and its host are 48 hours. Apparently, this period is reset every time the host and symbiote are seperated.
Average Strength level
Average strength level unknown, though the larger they expand the more weight they can lift.
Weaknesses
The Symbiote attached to the Edward Brock of Earth-2149 was shown to be dying after the zombification of its host; suggesting it cannot subsist upon dead flesh or tissue. Though this issue has never been addressed by its mainstream counterpart, there is nothing to suggest it could not also be the case.
All symbiotes seem to have a weakness against very large vibrations and heat.