An old RPG adage runs "never split the party". It's both to make life easier for the belabored DM and increase the odds of PC survival and effectiveness. It makes some sense indeed for the players to always have their PCs pool resources and capabilities, that's why there are adventuring parties after all. For the novice DM or one with a host of immature players it's a good tactic to keep everyone in the same mob sometimes DMing can indeed feel like "herding cats". After years of play it's my considered opinion that never splitting the party is cheating the players and the DM of a wider range of adventure experiences.
The DM needs to master 2 techniques to make splitting the party work: record keeping and the cut scene. With record keeping the DM must keep track of where and when PCs are active, PCs will quickly displace themselves in time given the opportunity to do so and the DM has to be accurate and firm in keeping track of this.
Note doors kicked in and bodies and loot left behind.
The cut scene should be used to create cliff hangers without otherwise upsetting the flow of play. A random encounter is much more exciting presented as a cliff hanger then the standard presentation and pretty easy to pull off with careful record keeping aiding the DM.
Additional tricks to keep splitting the party fun:
Verisimilitude in encounters: have encounters that make sense, more low level monsters present as opposed to high level monsters that always conveniently are the right level to challenge 6-10 adventurers of the dungeon level. Big tough monsters that folks get plenty of warning about so they can decide to gather the adventurers together since they can't be tackled by just 1 or 2 PCs.
A pair of ghouls is short work for all but the most inexperienced of parties but a lone fighter or 1 or 2 thieves will feel very differently about such an encounter than an entire party would.
Small treasures worth winning for 1 but not for 1 dozen.
The chance to harm allies. Keep descriptions of folks trying to creep down tunnels and go unnoticed vague. "You see three shadowy figures sneaking down the corridor avoiding the center of the passage. " gives a lot more room for misunderstandings and accidental assaults on fellow adventurers than dose "you see Mort, Nelson and Valdra walking down the hall". Check for surprise for each party, if surprised allow for a save of some kind and on the first round the surprised party can act they will act as if they were in a typical dungeon encounter (flight or fight). You have to be loose and fancy free with this and every now and then someone is getting fire balled by a friend.
Scouting missions. The quiet sneaky guys can move ahead of the rest of the party and check things out an hopefully not have to deal with major encounters. This is the easiest method of split part to encourage
Have players play some monsters. You want to see the dungeon beasties attack with cunning and awful ferocity, let one of the uninvolved players take the role of one or more monsters during an encounter; the fight will be more memorable for everyone involved.
When a wandering encounter comes chasing some of your friends down the hall it's a lot more exciting. Since folks can move around over a larger area of the dungeon they are going to be encountering more foes if they are not careful and possibly bringing them to their friends to deal with.
Let players do what they want. Don't let players act on knowledge their characters couldn't reasonably be privy to. It's safe to assume all the PCs at a table know about a trap when all the adventurers meet up at the local tavern but not while they are in two separate parties crawling about the depths until they are able to meet up in space and time. By letting players do what they want with the knowledge they have when the party is split up the actions of one player do not always immediately impact the play experience of everyone else at the table. The pesky thief doesn't' have to be ruining the game for everyone at the table with his exploits and failed pick pocket rolls if the whole party isn't present (the last one thief was seen in a campaign was his boots on the feet of a beggar a day or two after he went on a pub-crawl)
Get the players used to giving up time. Keep one fraction of the adventurers to no more then 15 or 20 minutes of table time.
Multiple characters per player. Let players run multiple characters if they wish but encourage them to split up by time sharing, the folks that can't bear losing table time will split up their characters or face large swaths of waiting for their turn.Sometimes players can end up playing the retainers and henchmen of other players, I like this arrangement but it's a tricky method that one shouldn't forcefully encourage.
With these techniques I had PCs running about on different continents, three time zones and multiple planes of existence all in the same gaming session, in a campaign that lasted for years.