This is a list of several groups who periodically host fleets open to the general public.
As at 2019, the Bombers Bar (BB) is in full swing. There are a number of people in specific corps that devote a lot of their game time to leading and supporting BB.
BB flies public Stealth Bomber fleets in which all are welcome. There is minimal/no politics and the fleet flies NPSI (Not Purple Shoot It aka anything outside of fleet can be shot). Some fleets include more than 100 attendees so it often creates some ethical issues if the fleet goes into allied space of one or more fleet members and the individual needs to decide whether they can engage allies/friendlies/blues.
BB runs some different fleets from roaming through space to using covert cynosural fields and black ops ships to drop into Null Sec and Wormhole space to blow up expensive ships and fleets.
Generally, the essential skill to join a BB fleet is to be able to use a Covert Ops Cloaking Device II which requires Cloaking IV. The ability to fly a bomber which can deliver bombs and torpedoes is also a mainstay of the fleet. However, fleets tend to require hunter/scouts, tacklers/bubblers, ECM, loot ships and more. More advanced pilots might fly Black Ops and other ships in support of fleets. Just make sure that you have the right doctrine/ship organised early for the fleet that you are attending.
Details on upcoming fleets, fittings, fleet instructions and joining comms can be found in the in-game channel (join 'Bombers Bar'). Usually each fleet will specify a form-up system and time. At the alloted time, the FC will update the channel Message of the Day (MOTD) with an extra channel in which to X-up to join the fleet. This involves entering the temporary channel and sending an X in the channel chat - someone will send you a fleet invite. Roams may start from the form-up point, other types of fleets might specify a staging system to start heading to as the FC starts to provide more instructions.
It is essential to be in comms to hear, sometimes at very short-notice, instructions from the Fleet Commander if a target has been found by hunters/scouts. Sometimes a blingy ship is found and the time to bridge/jump and engage the ship is very short. New pilots are always welcome but should expect to spend the first fleet getting used to the fleet mechanics to master landing effectively, delivering bombs, getting in on big kills and getting out safely. The environment is often very friendly though and worth attending.
Ship replacement, through Obombercare, is generous and funded by blingy loot that is regularly collected from wrecks during fleets.
BB is often an excellent opportunity to build killboard stats - to get involved in small or large-scale kills but also to build knowledge and skills which contribute to Eve Uni titles. It is also a chance to operate in a larger scale fleets and enthusiastic capsuleers.
Spectre Fleet (SF) is a public NPSI fleet (politics does not matter and individuals can decide whether to engage their allies/blues).
Having spies (spais) is an unfortunate part of public fleets but it is generally kept to a minimum. If a fleet is spending time in an area blue to one or more fleet members, there is an unwritten rule that fleet members won't give the game away (whether or not they participate in battles/kills).
SF flies many different doctrines in regular fleets and can be a lot of fun and a supportive environment. As with other public fleets, some SF fleets move quite quickly and can be a little confronting on the first occasion for new attendees. Any experience in basic fleet mechanics, coupled with the essential SF (or BB) fleet instructional videos, are quite helpful. It is important to note the Ship Replacement is not standard on SF fleets and prospective participants may want to check on the level of risk.
Details on upcoming SF fleets, fittings, fleet instructions and joining comms can be found in the in-game channel (join 'SF Spectre Fleet'). As with BB, carefully check the doctrine/fittings and the staging system to ensure that you are there on time in the right ship (and not being 10-20 jumps away as the fleet starts moving).
Vulfpeck is a primarily PvE fleet that operates small fleets of Confessors in C5 and C6 Wolf-Rayet Wormhole systems, taking advantage of the Wolf-Rayet system effects to take on the highly dangerous sleeper combat sites in ships that, at face value, look much weaker than would be thought necessary. Vulfpeck tends to only run one 4-hour fleet per week, however those fleets can reach 200 million ISK/hr/pilot, using surprisingly inexpensive and low-SP ships.
On rare occasion, due to the dangerous nature of wormhole space, Vulfpeck fleets may engage in PVP as well. Vulfpeck does offer SRP in situations where combat goes south.
FUN inc / Even Better With Friends [EBWF]
EBWF is another public fleet option with different NPSI fleets.
Founded in 2018 as a safe haven for small gang pvpers after the demise of Agony Unleashed FUN inc / Even Better With Friends is an EU TZ Nullsec PVP corp and NPSI group, specialising in nullsec solo, small gang and microgang combat who fight almost entirely in Nullsec.
They are a corporation in their own right and when the NPSI roams take place they roam freely, engaging whoever they like, and have created a no drama PVP community that roams Nullsec looking for good fights.
FUN inc / Even Better With Friends has an active discord community server which affords the community opt-in sub-channels for ship fittings, for timezone specific and NPSI roles which allow you to team up with other likeminded bloodthirsty PVPers and roam with FUN inc.
All the details can be found in the in-game channel (join 'EBWF public').
The Ancients is a new collaboration between various NPSI Fleet Commanders and potential brings together a number of fleets.
Arataka Research Consortium
ARC (in-game channel 'Consortium Operations') are a public group of 'defenders of humanity'. Their more core members are consistently active on the Roleplay forums, gathering and reporting information on the Drifters and the Triglavian invaders. However, for those interested in more actively defending humanity, ARC hosts public Triglavian Invasion fleets, taking 8-16 pilots in heavily armored battleships and battlecruisers to take on the Major Conduits and Observatory Flashpoints of Triglavian Invasion systems. Uniquely, ARC Triglavian fleets also offer publicly available ships, which are loaned out to fleet members for the duration of a fleet, so as to make their fleets more freely accessible to newcomers (without forcing them to buy and bring their own battleships). Similar to public Incursion fleets, ARC Invasion fleets are freely drop-in/drop-out; pilots can join and leave at any time (between sites) while the fleet is active.
ARC previously made a name for themselves as being one of the only organizations in New Eden to host periodic Drifter Hive Fleets, in which groups of ships fly into Drifter-occupied Unidentified Wormholes and attack their inhabitants head-on. These fleets are still held, however their focus has by now shifted more to handling the Triglavian Invasion.
Remember the EVE University Rules, including restrictions on attacking structures and involvement in any wars or pseudo wars. If in doubt, err on the side of caution so that all of our unistas don't inadvertently become war targets outside our rules. Although the fleets are NPSI, it is still very important to follow the rules and minimise engagement with our friends and allies (+5 to +10 blue status with Eve Uni or Ivy League). NPSI fleets are generally quite aware and supportive of fleet members not engaging their allies. In short, Unistas and Unista Alts should not shoot Unistas (unless permission is given).