My general take:
If your concept involves fighting with weapons instead of magic, you can probably do it in 4e, unless its something that is defined by mechanics and which has been specifically killed off in order to create meaningful choices. An example of that would be "guy who sneak attacks with a greatsword." Part of making weapon choice have consequences has been the decision to give certain powers to certain weapons. Greatswords have their own benefits, daggers and rapiers have their own as well. Making the choice between rapier and greatsword meaningful means that you can't get the benefits of one while wielding the other. If your desired character is one that falls into this category, you may benefit from a less mechanics-oriented character concept. If you were to change your desire to "maneuverable character with a greatsword who flanks with ease," that should be doable, particularly with the mobility oriented Fighter at wills coming out in Martial Power.
This is harder to do if your concept involves magic. In that case, there are a few archetypes that probably won't ever exist.
The first is the wizard who doesn't know how to hurt people. All wizards have a mixture of utility and damage, and it looks like that's just how its going to be, forever. Sorry. The best I can say in this context is that there are a lot of utility powers that provide utility AND do damage- for example, a spell that in 3e might have imprisoned your foe in a mystical cage will, in 4e, most likely imprison your foe in a mystical cage while lashing him with lightning. So if your goal was lots of utility, its available, but if your goal was an inability to do damage, you may be out of luck.
The second magical archetype that simply isn't going to be available is the mass summoner- the guy with an army of summoned creatures. This appears to have been a balance and table-parity oriented decision that is unlikely to be reversed.
There are probably a few more, such as the 3e style shapeshifting spellcaster (one who essentially abandons his physical form to gain melee strength but who doesn't give up spellcasting in payment), but that gives you the idea.
Leaving aside major reskinning (fighter reskinned as monk, etc) I guess there are four possible answers that cover most of the "I can't do X in 4e" comments.
1. Yes, you can. Read better. (This hasn't come up here, but it does sometimes.)
2. Yes, you can, but you may have to give up defining your concept in terms of mechanics and instead define it in terms of capability. (Rogue with a longbow -> Ranger, smart and tactical Fighter -> Warlord)
3. No, you can't, and the fact that you can't is for the overall good of the game. (Sneak attacking greatsword, Ubershifter)
4. No, you can't, but its likely that you will sooner or later. (druid, monk)