It seems clear that 4E really wants the party to have at least four PCs, so that all four roles can be covered. The official rules give tips on what to do when you can only have three PCs, but when it comes down to one or two PCs, the advice is pretty thin. For a single PC game, the DMG seems to punt, saying something like "you should probably play a leader or defender" and nothing else.
I'd like to be able to run one-on-one stories with characters in a larger, existing game, so I don't want to hear "use a different system." The larger game already exists, and the characters already exist, too, as 4E characters.
So far, I've found only good online ses of tips (which I will provide below as an answer) but I am eager to hear others — especially if they have been play tested. The ones I've found already appear to be theoretical only.
Best Answer
I've quite happily run one-on-one adventures with no changes from the base rules. A higher focus on minions is handy to come within the XP budget and access to personal healing is a must. It works better with defenders, leaders, and controllers than strikers. (Strikers really do require a party behind them to perform at their best.)
My own experience suggests that you should make it clear that "killing the enemies in open combat" is not the primary tactical motivation, which allows the player to bypass or subvert many encounters.
Instead of multiclassing, potions are an excellent healing mechanism, especially if potions are healing are converted to
healing wordlevels of utility. Alchemy, if made less of a gold-sink, is another excellent way to provide unusual resources to a character.