You know, outside of eliminating all the situations that require a cleric, trying to eliminate the cleric class serves no point. Otherwise, all the problems that the cleric had to put a band-aid on before are just going to be shunted for someone else to take care of. So now instead of the cleric casting all the healing spells, the wizard's doing it. Instead of the cleric casting invisibility purge, the bard's doing it. Instead of the cleric casting dispel magic, the ranger of all people is doing it.
Is a fighter type required? A rogue? A mage? Lack any one, and certain encounters just become infeasible. Some monsters just don't care about sneak attacks, and aren't overly vulnerable to spells. Traps are problematic for any group without a rogue. Your average purple worm is toast against any spellcaster whose spells rely on will saves to resist.
Now, of course, a cleric is generically useful; the fact is, everyone's going to need healing. Then again, druids, bards, paladins, and even rangers can eventually cover that arena, if only partially. Monks partially fulfill the healer role as well. Even beyond that, what's the big deal with some downtime for healing? Unless your DM is absolutely crazy with random encounters, waiting around a week to heal up shouldn't be that big a deal.
Is a cleric required? No. Is it more important to have than a few other classes? In a generic kind of way, yes. But just like if your party lacked a rogue, or mage, or fighter-type, certain encounters become more difficult, or near impossible to deal with. A party of a bard, barbarian, monk, and a druid is certainly going to have a number of difficulties (and even, hey, advantages) that one with a rogue, fighter, wizard, and cleric won't have. Take a cleric out of the equation, though, and the party should have a bard or druid to possibly make up for the otherwise lack of healing (or at the very least, a paladin or two). As for other stuff, about the only things that clerics have that no one else does would be the upper-tier Restoration spells, and raising the dead - none of which are particularly useful in the middle of combat, anyway. Dispelling magic is fairly generically available, while invisibility purge is easily replaced by glitter dust. Taking a cleric out of the equation means, to a degree, just having to spread the role out between the rest of the party.
Beyond that, cleric's still are fully capable of shining during a combat, between Hold Person, Poison, those half-holy damage Flame Strikes, and a number of other tricks. If somebody wants to play a cleric, but doesn't want to play support, then it would be good for the player just to remind everyone else they can do a few of the same tricks he can.
Anyway, no party should ever be forced to have a certain class in it; there should be a certain amount of give and take between the DM and the players. If no body want to play a rogue type, yet the DM keeps forcing traps down their throats, then the DM's doing a poor job of running the game for penalizing the players for playing what they want to. By the same token, if nobody want to play healer, yet the characters are regularly being slapped with random encounters before they can get a days worth of natural healing in, then that certainly interferes with folk having fun.
Anyway. I've been rambling on for way too long. Tired. Bah. Essentially, a game can be run without a cleric - just that the game needs to be modified for that. Even then, only slightly. A bard and a wizard, or druid and paladin, readily make up for a number of deficiencies that a lack of a cleric creates. If all of those are somehow lacking, well, the party sounds a bit homogenous, anyway, and will likely run into a few other problems then what would simply result from having no cleric.
But, personally, I love clerics. So long as there's an interesting enough pantheon/religion to work with, I jump on them. Anyway...gah...tired...later...ramble, ramble..
