Is normal (feat-based) multi-classing beneficial in D&D 4e? Is there a better way to achieve the same character design (a character with facets of two classes)?
There are some good multiclass choices, but aside from bards, the major uses for multiclassing are:
1: Get a decent encounter/daily power. Having the ability, as a melee character, to pull off a 1/encounter ranged power from Invoker, Warlock, or similar, might prove useful, and most characters can be well served by picking up a Leader multiclass just to earn a healing power 1/day.
2: Get a couple of feats. There are some feats that are class based, but have implications for other classes.
3: Get access to a new paragon path. A pacifist cleric might still wish to multiclass bard, to pick up the Lifesinger paragon path, for instance.
It's entirely possible to use the power swap feats--but usually it's not something you'd want to do.
The main mechanical benefit of feat-based multi-classing is that your character will still remain effective in his role. Hybrid characters might (ie, if you hybrid two controller classes together, you still get a pretty decent controller), but it isn't guaranteed.
The two main benefits as I see it is that 1) multiclassed characters are interesting because they can do something unexpected- the warlord who suddenly lets loose with a wizard-spell is a surprise to everyone the first time it happens. The second thing is that allows for events in the campaign to really have an effect on the character- one of my PCs multiclassed into spellscarred after being burned by a magical trap, for example.
It's certainly not as beneficial as in past systems, such as in 3.5 where it was virtually mandatory, especially if you wanted to qualify for a prestige class (many seemed to require multiclassing).
There is one class that benefits from it greatly - bards, with their Jack-of-all-trades nature, can multiclass via multiclassing feats into multiple primary classes, picking up powers from many sources if they wish. There's actually a PDF supplement on D&D Insider - not one that requires a subscription, if I recall correctly - that offers alternate paragon paths and epic destinies for bards who choose to multiclass in certain ways.
Very Rarely are feats so scarce outside the character optimization boards that you cannot afford to blow some feats on getting some powers from outside your class.
Getting another encounter power and a trained skill for a feat is pretty much a steal, the swap feats are okay as well presuming you want something from another class and that compliments what you are already doing.
It's a much better option than taking Skill Training, IIRC. As a wizard, I wanted to be trained in Religion for high knowledge checks as part of my character concept, since he was trained at a temple of Ioun.
It was much better to spend that feat multi-classing into Cleric or Bard than just the Skill Training. This way, I get a bonus daily use healing power.
If you don't want to roll a Half-Elf (side-note: I love how they're not "all the weaknesses, none of the strengths" of being a hybrid race that they used to be), the various multiclass feats have a lot of use. There are even more in Martial Power that can be used to grant class features across the board.
I think the feat based multiclassing in D&D 4e is probably one of the most elegant solutions. It allows you to do what people originally wanted - have elements from another class, with a primary base class. It also really helps differentiate between a Fighter-Thief and a Thief-Fighter, which prior multiclassing systems didn't do. It also avoids both the stacking and overlapping problems that prior multiclassing incarnations had.
With the introduction of the Hybrid classes, I would say it would be incredibly rare for this to be worth while. To argue against my point, often you'll find you're in groups that are consisting of mainly dps classes. Any strength-based class can pick up the Warden multi-class feat to gain the ability to mark everyone around them once per encounter. This could be incredibly useful for that one player that has a few more hit points than everyone else.
In addition, that person could take a few of the Warden paragons that have forms that allow for constant marking.
So I could see the pull for them, where you want to be 95% of one class type, but 5% of another, rather than 50/50 a la hybrids.
I agree with others that the primary benefit comes in access to other classes's feats, but I think there's an additional point worth noting - there's a few paragon paths (and complimenting feats and powers and items) which are specifically geared towards specific multiclass combinations. (I think the first was an early Class Acts: Warlord that focused on multiclassing into Infernal Pact Warlock and using polearms.)