Well, after playing Swain for quite some time now, and trying several different builds, I have decided to put my own here for the public to see. If you play Swain and are looking for new builds to try, I highly recommend you try this one. It is the one which has worked best for me, and I hope it will work for others as well.
As is customary, I have taken a screenshot of my recent matches with my build. This is what you can look forward to:
The reason I choose to max out Torment (Swain's E) first is because it's your best move to harass with. It makes laning easy, because it doesn't cost too much mana, does nice damage, and is great for your damage output due to its %damage increase debuff. It's nice to have Nevermove (W) early on in case you're in danger of being ganked or you're trying to gank, but if you level it up too soon, you will have mana problems. Of course, your Q is great for damaging champions quickly and the R is a must, so the priority after level 4 is R>E>Q>W.
I bring Ignite because it complements the rest of Swain's DoTs well (and as far as I know, it is also amplified by Torment's %damage increase effect), and I bring Flash to get out of losing situations quickly. I can see many others working with Swain. What you bring is your decision, it's completely based on one's preferences.
There are many situations of which I could spend days typing, so I'll just summarize the main things I do as Swain.
As Swain, I personally recommend you to either mid or solo top. These allow you to level quickly, so you can help your teammates in other lanes and carry your team. If you play him correctly, you won't die at either.
At solo, stay as far away from the brush as possible while still being close enough to the minions that you get experience. I like hugging that little wall in between the river and your tower. Staying there means you're far enough from the brush to avoid a gank, close enough to the minion wave to recieve exp, and close enough to your tower to run into it's range before enemy champions can do anything lethal, but use good judgement. Don't try to hit minions from too far outside tower range, because it usually means death.
Mid is where Swain can really shine, though. Against most champions, Swain can get a few kills before mid-game. If your team is good with MIAs and you're careful enough, you shouldn't die.
Early game, whether soloing top, mid, or laning with a partner, you will want to harass your enemy with Torment while staying near full health (easy with your health regen) and last hitting minions. If he is dumb enough to harass you with an auto-attack or an ability that forces them to get moderately close to you (given that the ability won't cripple you too much), counter-harass with Torment. At level four, you should be able to get a kill if your opponent has around half health, usually (unless you're in the solo lane, in which case I would play it safe until level 6 and one of them gets within tower range). When your opponent is at the edge of the range of Nevermove, cast it slightly behind them, run in with your E as soon as you cast it, cast Q, and ignite them. After that, they should die either from the "burst" or the lingering DoT from Torment. If they dodge Nevermove, back off, you won't get them, and if you pursue, they'll be more inclined to base. If you have trouble doing this at level four, wait until you have your ultimate and just tack that on to the end of the combo or right after you E. It adds enough damage to usually guarantee a kill unless they have extra health or magic resist.
As the match turns into more or less constant teamfights, your survivability will depend on how well you can time your ult and if you're good at leading opponents into your snare. As a teamfight begins, I usually snare the enemies charging in, pop my ult, and nuke the nearest squish (provided that I see the opportunity to do so. You don't want to just run in to nuke one and then die, because they will probably survive if they're any good). If you get targeted, run. Although your ult heals you quite nicely, you are not a tank, therefore you can still be burned down pretty quickly in a teamfight. Even while running, you still do nice damage to the enemies with your ult anyway. Your W can also be used as a nice support. If you or a teammate is being chased, try to snare the enemy champion trying to kill him (Your Q can also work to this effect, though it's less effective). The same thing works the other way around: If an enemy is trying to run away, snare them to ensure the kill.
Also, just as a general rule of thumb for your own good, I would recommend turning off your ultimate when you are around 20% mana. This gives you plenty of mana left over for you to use to escape a gank with your W or finish off an opponent with E and/or Q if you need to. If you find yourself lacking mana at times or not being able to stay in raven form long enough, grab the blue buff whenever you see the opportunity. It really helps and is almost vital in long teamfights.
Note: If you think you are about to be stunned, suppressed, etc., don't be afraid to pop your ult. It may be your only chance for survival at the time, and you can't activate it while stunned. Better safe than sorry, and it has a low cooldown anyway.
Swain, in my opinion is an all around good champion. He has nice survivability, great damage, and he can easily carry a team if you play him correctly. This build is just my take on how he should be played. I am open to ideas you may have on improving this build. Comment and vote please! Enjoy!