Strangers in their own land
Indeed, many roleplayers nowadays find themselves stuck on an RP server which has seen better days. The community which used to be so vibrant now seems as though all the old roleplayers have either given up or gone elsewhere. They, too, wish that they could have fun acting in character like they used to, but nowadays it's all about so many Badges of Justice and Arena Points that they, too, find it difficult to really get themselves in the right mood for roleplaying.
If you're like me, you want to raid, PvP, and do everything the game has to offer, but you don't want to give up roleplaying to do it. For a long time I thought this might be a pipe dream, that no one on my RP server had time for RP anymore. I posted my wish on my realm's forums and asked my friends if they knew any guild like this, all to no avail. Finally, I gave up looking and began investigating other servers that I might transfer to. I also investigated a couple guilds I hoped might work, but found that none of them really suited me -- until finally I stumbled upon the right person with the right advice: the Guild Master of the raiding guild I was trying out used to be an avid roleplayer herself, and she recommended a full-time-RP guild she knew of. This new guild does everything in-character, from PvP to raiding Karazhan, and it creates an entirely different atmosphere which I enjoy a great deal. They're a gem of a guild surrounded by a majority of non-roleplayers on my server, and they have made me very happy to stay where I am rather than look for a new home.
Hidden bastions of hope
Chances are that no matter which RP server you play on, no matter how depressingly rare it may seem to find another roleplayer, small pockets of serious roleplayers remain, waiting for you to seek them out and find them. The problem is that they may not be very inclined to advertise their little group out where everyone (such as you) can see. Many roleplayers don't really feel welcome on a roleplaying server, oddly enough. It's as if they are the last remaining exiles of a once noble civilization, and they have to just cling to one another in order to survive. They may feel as though their style isn't so popular anymore, and even if they announced themselves to all the world, it might draw too much unwanted attention.
In your quest to find such a guild, however, you have several tools at your disposal. The first, most obvious idea might be to post your ideal guild description on your server's forums in the hopes that someone will see it and match you up with the guild that fits. Sadly, I must caution you not to expect too much from this. Many of the best players of any sort reject the forums entirely as a cesspit of degenerate and useless nonsense. You might be lucky enough to find someone intelligent there, however, so give it a try.
The guilds who advertise in the various chat channels also aren't likely to be very reliable in my experience, and are best avoided. Those of you who are especially patient and adventurous may prefer to meet your roleplaying friends in the wild this way (as many experienced roleplayers did long ago before we discovered forums and guides and such), but for a newcomer I do not recommend it.
A journey through the grapevine
Most likely, your best bet will be to talk to as many reasonable people as possible, and rely first and foremost on word of mouth. Formulate a clear explanation of what kind of guild you want, what kind of playstyle you think will meet your needs and then ask about to see what people know.
But here's the most important thing: don't just ask your friends - be sure to go out of your way a bit to ask people you don't normally talk to all that much. That's not to say you ask just anyone on the street -- think of people who seem well connected, reasonable people, whether or not they are avid roleplayers. Feel free to ask your friends of course, but remember that if you spend a lot of time with them now, then you probably know most of the people they know already. It's the people you've met a few times but haven't talked to in ages who might be able to help. Send them a note asking how they've been and what they're up to, and... "by the way, do you know a guild that fits this description...?"
Of course no guild will be 100% perfect. It's important to think about what kind of guild you really want, so that you can keep guild hopping to a minimum, find what will make you happy sooner, and spend time developing relationships that will last.
Think about these questions: How much do you want to roleplay? How do you prioritize your various activities in the game? Are you always in character? Or is raiding priority with a side of RP now and then? What do you want to contribute to your guild, and what do you hope to receive? How important are all these questions in relation to the other guild issues?