Red vs Blue (RvB) consists of two hisec corporations - Red Federation and Blue Republic - which maintain a constant state of mutual war. Recruitment is open to anyone (just submit an app in-game), and together, Red and Blue form the most active PVP corporation(s) in Eve. The PVP is good-hearted, newbie-friendly and generally well balanced (at least as much as it is possible to be in Eve). Many RvB members are new to PVP, and cheap ships such as t1 frigs and cruisers are encouraged, although almost anything goes. RvB enforces a small number of rules (such as no podding, no ECM, and no neutral logistics) designed to keep the PVP fun and remove elements that lead to too much station camping or frustration. The success of these rules isn't absolute - in my time for example there camping opposing HQs with battleships was fairly commonplace - however they are fairly good at tweaking them to keep things fun, and the end result is constant, fun PVP pretty much around the clock.
What kind of person is RvB good for?
First of all, it's a great place for newer players looking for some high-concentration exposure to PVP on a budget; you can join RvB for a month or two and get yourself on hundreds of killmails, lose dozens of ships, and come out with a reasonable idea of what you're doing. You'll still have to pay for your ships for the most part (occasionally free ships will be given out for a special event), however if you keep your fits cheap this shouldn't be too much of a burden. Expect to lose a lot of them, but it will be worth it - most fights will be pitched battles where scores of frigates and cruisers die on either side, and even a rookie can feel like they are contributing meaningfully to the success of their fleet. Currently RvB limits their PVP to certain constellations, meaning you can still mission safely on the side if you only have one character and are in need of the isk.
RvB also has plenty to offer more experienced pilots - your opponents are a fairly known quantity, and taking on superior numbers and coming out on top is a feeling we can all get behind. That said, you need to be prepared to take some risks (and some losses) in the name of sportsmanship too - if you turn up hoping to pwn n00bs in your untouchable nanoship all day then you'll probably find sentiment in the corp starts to turn against you (at which point the traditional thing to do is ragequit from RvB, wardec them as a third party, and then do it some more). While cheap ships are encouraged, you're free to fly whatever you want providing you're reasonable about it. Occasionally the opposing FC may ask you to ship down if you keep bringing something they can't engage - if nobody can fight because one side has both the bigger ships and the bigger fleet, it's no fun for anyone. All in all, an experienced PVPer with a relatively laid back attitude will find that RvB offers far less waiting, far more fighting, and far fewer cloaky sabre or instalock gatecamps than you're likely to find anywhere else.
Finally, RvB is an excellent destination for anyone with limited PVP time; you can quite easily log in for half an hour, find a fight, and then log out again. This is something you can't say about many other corps, particularly larger nullsec alliances which may take that much time just to reach an area which isn't blue to them (not to mention form-up time, finding targets, etc). RvB is also alt friendly, so you can easily put a low-skilled alt in there for the occasions when you don't have time for a longer roam, while keeping your main in another alliance for the times when you do.
Tell me more about the PVP!
Most of the PVP in RvB happens in fleets of about 15-20, usually with a mixture of t1 frigates and cruisers. The fleets tend to be roughly balanced by mutual consent, with the smaller fleet shipping up slightly to make up for their lower numbers. Complete fairness isn't guaranteed, and often fleets will need a little encouragement to not bring a superior force (I put this down in part to our natural tendency to overestimate opposing fleet sizes while underestimating our own). Still, the fights tend to be far more even that what you're likely to find elsewhere. Most of these fights take place within two or three jumps of the two HQ systems (currently Autaris for Blue and Hageken for Red), although the potential PVP zone is slightly larger.
In addition to these ad-hoc fights, the corps also organise arranged fights (coordinated by FCs via the RvB command channel) - these follow a similar format but are arranged ahead of time, often with agreed gang sizes or compositions. Some of these take the form of special events, such as free-for-alls, themed battles, wargames and the like. During the month that I was in RvB, I participated in a hilarious rookie ship free for all as well as a cruiser brawl that lasted for hours and resulted in hundreds of kills on either side (every member was given their choice of 10 t1 cruisers with t1 modules, and the two corps battled it out until all ships were destroyed). Anothr recent example was an event titled 'sink the Bismark', in which the Reds attempted to escort a faction battleship safely through hostile space and the blues tried to stop it - by any means necessary! You can read about the event in blog posts by Mangala and Tgl3, two of the main Red FCs.
For those who are looking for solo PVP, there is plenty of this too. Some RvB pilots solo almost exclusively, and there are people of all skill levels asking for arranged 1v1s in local on a fairly regular basis (RvB has a rule against interfering in an arranged 1v1, which will usually take place at a planet). Ad-hoc 1v1s are also prevalent, and due to the relatively small operational area the chances of running into another solo pilot are high. For those who like to fly on the wild side, you can also try to pick off stragglers or even take on whole opposing gangs, however the RvBers always have a home station close to hand and are notoriously quick to ship up when a juicy target presents itself - if you engage a group of frigates solo in your battlecruiser, don't expect them to stay just frigates for long!
When the corps are wardecced by a third party (which happens fairly often), they will generally set aside their differences when a war target is around (known as purple status) and focus on the third party target. In this there are no holds barred, with the usual rules regarding podding, ECM and neutral logistics thrown out the window to make life as miserable as possible for the unfortunate war target.
From time to time the corps also run joint roaming into local lowsec or nullsec areas, including their popular gankednight roams which are open to members of the public. These can be a welcome change of pace as well as a chance to PVP outside of the usual RvB environment, and they are incredibly fun. However I should warn you that gankednights are strictly a relaxed affair, and while they generally feature epic fights, serious business they are definitely not.
But Wait
While I enjoyed RvB immensely, I'd be doing them an injustice if I tried to pretend they were perfect. The truth is, a large proportion of RvB members are casual players or are new to PVP (not all, but many). While this is excellent for people who are of a similar mindset, those who take their gaming more seriously may find themselves frustrated at times. That isn't to say you won't enjoy yourself - you will, but you'll need to accept that your corpmates probably won't take things as seriously as you do, and while RvB has some excellent pilots you can't necessarily expect the same level of competency from all of your corpmates as you might in a more traditional PVP corp.
Many people join RvB because they simply want to be able to log in and find a fight with minimum effort - after all, that's something RvB is great for. One side effect of this is that it can be quite difficult to get people to volunteer for key positions. It's not unusual to have plenty of members online, but nobody willing to step up to FC the gang. This leads me onto another point in that if you know how to lead a fleet and are willing to do so, you'll probably find yourself FCing gangs much of the time simply because if you don't nobody will. This isn't really unique to RvB to be fair, but it can cause some frustration when you log on looking for something low pressure and end up sitting in the hot seat.
Don't let these facts put you off though; I include them in order to give a balanced review, but my experience in RvB was a very positive one - I'd definitely join them again if I found myself in a similar circumstances. What I would add is that if you do join RvB and find yourself in the above situation, with plenty of people online but nobody willing to lead, just do it. It's not as hard as you think, and nobody is going to hold it against you if you make a bad call - they fly cheap for this very purpose and the alternative is sitting in station doing nothing, which isn't fun for anyone!
You can find more information about RvB on their forum, or by joining the in-game channel R-V-B.