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So, looking to run a D&D 4e adventure with some of my friends, but we've only got the four of us — myself and three players. The adventure I want to run, named the Slaying Stone, recommends at least five characters, and since I'm the DM, it's bad practice to play a character myself. We also have no desire to include other people as we mesh well together as it is.

How would you lovely people recommend dealing with such an issue?

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One big issue with not having a full deck to play with is party/class/roll synergy. It's going to be infinitely more difficult for your players if, for example, they all roll Controllers, so they should think about what rolls should be covered and what you could do without.
DMG, page 31 has a nice little excerpt about that;

Small groups can’t cover the four basic character roles. If you have only three player characters, you can do without a controller or a striker at the cost of a little damage output.

That isn't to say you have to have a Defender and Leader, although it would be a good idea, but they need to consider what they are giving up for each roll that they don't cover.
Character's Skills might also be worth mentioning here as well. If they all, more or less, choose the same skill set they're going to have a tough time with skill challenges.

So that's something for the players to think about.
Now for what you can do as the DM. You have a couple of options here.

One thing you can do is use the XP budget table on page 57 of the DMG to adjust each encounter to compensate for the lack of PCs. Instead of adding monsters to fill your XP budget, you remove some. You don't have to hit the exact value given, just as long as you're in the ball park you should be good.
For instance, your XP budget for 3 level 1 PCs would be 300, so for any level 1 encounters in your adventure you would need to remove monsters until the total XP value of the remaining ones is roughly 300.

Another thing would be leave the encounters as they are but stagger the amount of monsters on the battlefield, have a some tied up with some other task and join in the next round or two. If you have a large battlefield you can simply put some on the very edges so it takes them a round or two to even reach the PCs.

In the case of skill challenges I'm not too sure. You could maybe try reducing the complexity level by 1. It depends on the diversity of your player's chosen skills as to whether or not you think they should have a chance of success if you leave it or change it.

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Reduce the number of monsters after assessing how optimised the party is. The minimum and maximum levels of optimisation and (especially) designed cooperation matter more than the number of players.

Adventures, especially early adventures are very particularly staffed with monsters. Some encounters are silly, others are very very hard. For a smaller group playing through an established adventure, encourage them to optimise their group (link1), (link2). You'll likely want to re-staff the monsters anyways from later sources, re-skinning as necessary to achieve awesome combats. Just include one or two fewer of these newly-upgraded monsters in the first tests.

A group which is designed to work together should require minimal tweaking from the adventures, save for the normal updating to the latest versions of monsters and other sanity checks. If I was running this for the group, I'd allow unlimited rebuilding of characters on long rests, with equipment by the rules (level-1, equal level, and level+1 magic items, with gold and common items totalling level-1 worth), and only worry about dropping plot-significant or narratively interesting items. That way, the group can adapt to challenges and, in a sense, auto-balance without needing excessive in-world fictive justification for those changes.

If it was my group, I'd probably recommend something like: (Ardent or Shaman), Warlord, Thief. By carefully ensuring that the Ardent and Warlord know how to provide the best setups to the thief, all three of them can do "better-than-thief" levels of damage with the MBA granting capabilities of the two leaders. In this instance, I would absolutely suggest that on a granted attack, if the granting player isn't doing anything, to allow the granting player to roll the dice, but that should be seasoned to taste. While more interesting combinations are possible here, this is a very simple setup that should make short work of the "default" difficulty, while providing a fascinating tactical and technical challenge to your players. (Working out the narrative of the group would also be fascinating and could be very very neat, but that's an answer to another question.) This level of optimisation is likely overkill, and so a fair chunk of "dialing in" will be necessary to figure out the exact comfort level of the group. The offloading of items onto the players is mainly a way of making it so you don't need to worry about boring build-specific items, and so you can focus on wonky/interesting narrative items which reflect the impact of the character's actions on the world, rather than obligatory items to keep their math correct.

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Purple Monkey's answer does a good job explaining how you can adjust the encounters to accommodate a different number of players.

I'd like to add to that answer by responding to a different part of your question, though.

GMPC's Are Okay

You say "since I'm the DM, it's bad practice to play a character myself", but I can tell you from experience that this is not true. It can be difficult, and it may not be the best option for your game, but you should at least consider it.

I'm currently running a campaign with myself as DM and three players, and I play a fourth character. Not only is it working out fine, but I'm having fun and the other players enjoy my character.

Of course, that means that my campaign only has four characters, which is still not five. I write custom adventures, so I don't have to adjust published adventures, but I still have to use the XP budget to guide me when creating encounters.

Even though using a GMPC in campaign doesn't save me the effort of adjusting encounters down from five, it would still be worth it even if it didn't add to the fun, as four characters allow you to cover all the party roles better than three.

How can I GM and play a PC without spoiling the fun? has some useful answers to help you think about this option, including one where I elaborate on my experiences.

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    \$\begingroup\$ FYI the question's been clarified: it's three players + 1 GM, so a single GMPC would not bring the party up to the advised 5. (But as other answers point out, 4 could manage it, potentially with adventure adjustment.) \$\endgroup\$ – doppelgreener Nov 6 '14 at 8:02
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The DMG has rules for including a Companion character, which can fill in the 5th slot. It's probably the easiest way; Companions have very limited options and are really easy for anyone to play as a second character, but they are roughly as capable as a full-blood 5th member of the party.

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Another possible option is to just run the adventure as-is. 4e characters are very tough, so dropping from 5 to 4 players still leaves them with plenty of resources to handle each individual encounter.

There are two exceptions that I can think of, off the top of my head. One is if the adventure has parts that require 5 players, such as a chess-puzzle missing five pieces, or a 5 clues that need to be pursued at the same time.

The other is if the adventure won't allow the 4 adventurer's to rest once they run out of stuff (dailys, surges, etc), which they probably will a bit earlier than a 5 player party would. There should be some buffer already to account for an unlucky 5 player party, so your 4 player party should be able to handle it. Though the margins will be slimmer, than if they had an extra party member to pull on.

As long as the party keeps in mind that the encounters are going to be tougher than usual, and plan accordingly, I think they should be able to handle it.

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  • \$\begingroup\$ FYI the question's been clarified: it's three players + 1 GM, so that's a drop from 5 to 3, not just 5 to 4. \$\endgroup\$ – doppelgreener Nov 6 '14 at 8:01

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