Hybrids are complicated, especially if you don't have the Character Builder. They're a lot closer to Multiclassing than 4e's actual Multiclass system. You take two classes, take half of the hit points from each class, add them together, add your Aunt's telephone number and divide by the square root of zero. You lose most of the minor class features from each class, but you can gain one of them back later by taking a Hybrid Talent Feat. You get a few skills from each class, but some classes get extra skills. You take three points from your IQ and add it to your pants size. You get one At-Will from each class, and you can cherry-pick your Encounter and Daily powers from either class. If one of the classes uses Power Points, you can choose an option that makes them more like normal powers. You get all the weapon proficiencies but only the lesser of the armor proficiencies. If your paternal grandmother was a Half-Orc, you also get a fruit basket and a three-legged newt named Nadine. Or something like that.
Hybrids are great for jack-of-all-trades characters, but it's hard to come up with an optimized combination that works really well. I foresee them being used far more in roleplay-heavy campaigns than in combat-centric games. You can come up with some great combinations if you really work at it, but you'll still be giving up something somewhere. The difficulty is that the two classes need to have several points of synergy; specifically Primary Stat, Armor, and Weapon.
Of course, a Fighter/Wizard sounds awesome. You can rush into battle, slashing everyone around you, and launch fireballs at those farther away. But Wizard spells are based on INT, and you put all your points into STR and CON so you could survive the melee. You need to use your wand to cast that fireball, but your hands are full with your sword and shield. And Hybrids only start with the lesser armor of the two classes, so you're going to get cut to ribbons rushing into battle in your Wizard robe. Sure, you can take a Hybrid Talent Feat to regain the Fighter's normal Armor Proficiencies, but that's a feat that could have gone toward something else.
On the other hand, some classes work together pretty well, but upon closer inspection seem sort of pointless. I started putting together a CHA-based Warlock/Sorcerer, and it was looking pretty good... the stats, armor, and weapons all worked pretty well together. Until I realized that neither class was really adding anything to the other. The two classes are too similar - either way you're firing blasts of arcane energy from a distance. Unless there's a particular roleplay reason your character has studied the two fields, you'll probably be stronger as a full-blood Sorcerer or Warlock.
Now I'm not particularly good at optimizing characters, so I'm not going to run down a list of the best Hybrid combos. (The WOTC forums are probably full of cheesy builds by now anyway, so try there.) Instead I'm just going to mention a few observations, and notes about combos I'd like to try. If you want a quick reference to help you decide what might work, I put this together: Classes and Builds. It's a list of all the different 4e classes, the suggested primary stats, and the races that match the primary stats. It might help to have all the information in one place.
Hybrids lose most of the features you automatically get with that class, unless you take extra feats to get them back. So the best Hybrids are ones where you didn't use the class features much anyway. For example, Rogues keep Sneak Attack, which is of course their best feature. But they lose First Strike, which is painful. First Strike allows Rogues to use their Sneak Attack in the opening round of battle, and a crafty Rogue can change the entire dynamic of the encounter if they use the right power on the right enemy. My buddy Rick once took out the boss in the opening round, which left the DM cursing. So most Hybrid Rogues will want to take the First Strike Hybrid Talent Feat.
Meanwhile, my Archer Ranger Voranna hardly ever uses most of her lesser class features. Of course she uses Hunter's Quarry all the time, but Hybrid Rangers keep that. The features she would have lost are Prime Shot and Defensive Mobility. Prime Shot gives you an attack bonus if you're the closest ally to your target. That's fine for melee rangers, but Voranna tries to keep as many allies as possible between her and the enemies. Defensive Mobility gives her a bonus to AC vs Opportunity Attacks, which can be very useful in certain situations, but in five levels I've still yet to provoke an OA. So while Voranna's not a Hybrid, I very well might not have noticed if she was.
Hybrids get one At-Will from each class. Keep this in mind. Some characters have a tendency to use the same At-Will every round, while others have cause to use both. My Voranna uses Twin Strike almost exclusively, so she wouldn't have minded giving up her second At-Will for that of another class. But a Cleric, for example, might miss having both Astral Seal (which is very useful but doesn't do any damage) and an actual Cleric attack power. The worst is the Hybrid Druid, who no longer gets that extra At-Will for their alternate form. I hope they errata that, but as of this writing a Hybrid Druid is pretty limited IMO.
A lot of players are talking about making Hybrid Rangers, because Twin Strike is one of the most coveted At-Wills in the game. Other players are condemning that combo as pure cheese, but welcome to the world of D&D.
As I mentioned earlier, Hybrids only get the lesser armor of the two classes. However, the armor prof for the other class is regainable with the Hybrid Talent Feat. This makes Paladin a particularly attractive choice because you're only one feat away from plate armor. So you could take whatever you want as your primary class, and use the Paladin simply for the armor.
Your skills are a mix of the two classes, but some combinations yield more skills than others. If you want a skill-heavy character, you might consider making a Hybrid Rogue, as they get two more skills than the norm. Bards and Rangers each get one more skill than the norm.
Personally, I'm itching to abuse this system with a character so versatile that she's not even playable. Have a hybrid that also takes multiclass feats. Make her a Half-Elf so I can take her Dilletante power from a third class. Make one of her classes Bard so I can take even more multiclass feats. And so on, until she knows how to do a little bit of everything (and sucks at all of it).
Some combinations suffer or excel simply depending on which class you want to put in the background. For example, I've been considering making an Elf Ranger/Rogue, or possibly a Rogue/Ranger. Yeah, same thing, but stay with me here. With either combination, I'm going to want the following feats as early as possible:
Lethal Hunter (+ Quarry Damage)
Weapon Focus Longbow (+ Damage)
Weapon Expertise Longbow (+ Attack Rolls)
Treetop Sniper (Elf Only, Use Longbow for Rogue Powers)
First Strike Hybrid Feat (Have Combat Advantage at start of battle)
Backstabber (More Sneak Attack Damage)
Improved Initiative (+4 Initiative)
The first three are all I need to have a happy archer at level 4, and I already mentioned the Hybrid Rangers don't lose anything that I'll miss. But the other 4 feats are fairly important to have an effective Longbow Rogue, IMO. So my plan would be to simply forget the Rogue part until I'm level 6, other than the extra skills. Of course, this also means I can't take whatever else normal archers would be taking from levels 6-10, but them's the breaks with specialized classes.
Now, if I were to do it the other way around, emphasizing the Rogue over the Ranger, I'd probably want to take Backstabber and First Strike early on. I'd forget the bow altogether at first, and probably wouldn't even buy one until I had the Treetop Sniper feat. So for the first 4-6 levels I would act as a normal Rogue, my only disadvantage being that because of Hybrid First Strike, I'm starting one feat behind most Rogues.
The third way to approach this is to embrace the Hybrid - take Treetop Sniper first, because the combo is built around that feat. Then just live with the fact that I'm not going to be as effective as either class for a few levels. Maybe I'd use my 1st level experiences to decide whether I want to emphasize the Rogue or Ranger feats early on, or I could just alternate them.
Or course, this doesn't matter so much if you're in a campaign that lets you start at a higher level. But I've been playing for over a year and I still haven't played a character over level 6. So the order of feats at early levels is critical to me.
So in short, while you certainly can build some highly effective builds if you do the research, IMO Hybrids better thought of as flavor for people who want to play versatile characters. But useful or not, Hybrids are definitely one of the more interesting things in the PHB3.