AD&D had a rather different multiclassing system than 3.x and 4E. You picked two (or three) classes and leveled up in a gestalt of those two, splitting XP between both. 4E works a lot differently, but having just multiclassed my fighter into the cleric class (which is perfectly viable), I wonder what else works really well. So let's go through the multiclasses AD&D2 allows:
Fighter/Thief don't line up the prime stats nicely, but is still nice. A tempest fighter can get the dexterity to qualify for the Sneak of Shadows feat, giving him training in Thievery, and is probably using light blades that work with Sneak Attack. That's a nice burst of damage once per encounter. Going the other way around, a Brutal Scoundrel easily qualifies for Student of the Sword, giving him a +1 to hit with a (one-handed) weapon once per encounter (which also marks the target, but eh). You probably don't want to multiclass much further, except maybe to take utility powers from your other class - making a rogue a little tougher, or the fighter a little more sneaky.
All in all, playing a sneaky fighter is quite possible.
Fighter/Cleric is an excellent choice. Your prime stats can match perfectly, not that it matters much for the initial feat. A fighter can (and should) take Initiate of the Faith to heal an ally once per day. A battle cleric won't mind a +1 to hit once per encounter and an extra skill. Neither have to bend over backwards to get the stats to qualify either.
The future for a tough guy who didn't qualify for paladin school is still bright in 4E.
Fighter/Mage is a tough one. Neither gets much use out of the prerequisite for the other's multiclass feat, and the feats themselves are pretty non-synergistic. However, Arcane Power introduces the Learned Spellcaster feat, which gives you ritual casting. That and some useful wizard utility later on could give a fighter a dash of wizardry. He still has to scrounge up 13 Int for the feat, but that's doable.
Seriously, I'd recommend a Swordmage.
Mage/Thief No stat synergy here either, and the rogue has a harder time justifying both 13 Int and 13 Wis to qualify for Learned Spellcaster. I suppose a Wizard could be slightly interested in the Sly Dodge feat - giving him a bonus against OA:s.
I'd look into playing a Rogue/Warlock or even a Rogue/Sorcerer. Those feats aren't fabulous, but the stat requirements mesh well with what you already have. The Assassin is also relatively magical, though in another way than a wizard.
Cleric/Mage gets you a Wizard with a daily healing ability, or a Cleric with rituals (this one has to take some Int it doesn't need much). Again, you probably don't want to take attack powers from the other class, but utilities can be useful.
Cleric/Thief - no stat synergy, consider whether you want a healing Rogue. A cleric that can sneak attack with a light blade isn't all bad, but there's nothing amazing here.
Fighter/Druid... Fighters get no benefit from turning into a beast at-will, unless your DM is generous. Druids don't use weapons, and thus can't use the +1 from Student of the Sword. Hilarious. Battle Awareness - slap an adjacent enemy that shifts or attacks an ally - is at least moderately useful, but if your druid is in melee with enemies, they probably want to beat on him anyway.
Consider a Warden.
Fighter/Ranger doesn't even exist (thanks to Anonymous for pointing out that I had misread "Cleric/Ranger" in the comments), but it could work. Admittedly, the tempest fighter is close already, but what Ranger would say no to a +1 to hit once per encounter? A Fighter can pick up Warrior of the wild and kick arse with Hunter's Quarry. Stats line up perfectly.
Still, I wonder what the point is, fluff-wise, since the tempest fighter is already there.
Cleric/Ranger is the last of the two-class multiclasses. A ranger has the Wis to take the multiclass cleric feat, and a Battle Cleric will easily qualify for Warrior of the Wild (ranger multiclass) which doesn't have weapon restrictions and thus works just fine with cleric weapons. The character can then go on to take attack powers if he's going for battle cleric (both use strength), but note that many (but not all) ranger powers require two weapons, a beast companion or a ranged weapon.
Verdict: Cleric multiclass is as awesome as always, not huge potential for further multiclassing.
Fighter/Mage/Cleric is hard to do straight, since you can only take multiclass feats for one class. There is a background (Windrise Ports) that lets you multiclass into two classes, and of course the Bard can take as many as he wants (but then you have to start as a Bard). Given the background, starting as either Fighter or Cleric and taking the other two could be useful, as shown above.
Fighter/Mage/Thief has the same issue as the other triple-class, but works as stated above for class pairs if you can pull it off.
Verdict: Not shabby. Meleeist/Caster has issues that can be worked around sometimes, sometimes not. Druids are just weird, being melee beasts based off Wisdom. If you want to say that you're playing a Fighter/Thief, it is doable.