I'm just going to think out loud here for a minute:
One of the main strengths of BTC is that it is decentralized: nobody can arbitrarily print a whole lot of BTC and devalue everyone else's. BTC also has benefits like being nearly untraceable and potentially anonymous, as well as being irreversible, but those benefits are largely seen by cash (BTC is better at them, granted, but you could make do with cash, as people have done for ages).
The biggest forms of fiat exchange are cash, check, and credit/debit card. The most challenging group of people to spread BTC to is the less tech-savvy, especially older, demographic; these people have no problem with transacting using at least one of those three forms. Thus, it would be really nice if BTC could approximate the functionality of those three forms of payment. To that end, consider these three things:
Cash: There already exist paper/coins backed by bitcoins in the blockchain. Presently they are just novelty items, in the same way that a proof coin of a circulated denomination is a novelty item--it has a face value but is worth more for numismatic reasons. For the physical bitcoin to take off, it needs to have some standard visual appearance and some way to easily verify that the coins in the block chain backing that bill/coin are both present and uniquely assigned to that coin. This requires trust in whomever prints/mints the physical bitcoins. Also, they would probably be illegal in the US, since federal law prohibits any person, corporation, or government from issuing currency, other than the federal reserve (luckily, they aren't yet considering bitcoin mining as issuing currency, since they don't really accept BTC as currency it seems).
Check: It would be fairly straightforward to make a book of checks where instead of a routing/account number, there is a private key (or at least most of one). A user could write a check and provide the rest of the private key, as if it were a PIN, then TRUST the merchant to only take the amount the check is for. I think the trust towards the merchant is reasonable, since we already do that when swiping credit cards/writing checks, and since there is a paper trail to easily show the amount that the check should have been for. There is also the issue of trusting the check manufacturer not to take your money, but this is also not a huge issue. With checks, no attempt at anonymity is really made, so tracking down and confronting a scammer is easy; this contrasts with physical coinage, since the first person to use it trusts the minter, the second trusts the first, and so on, until the chain of trust is so long that it is probable that someone is untrustworthy.
Credit/Debit Card: A credit card by its nature requires a backing institution. For credit cards, I guess we just need a bitcoin credit company to spring up and start offering on-demand purchases with bitcoins on credit. The form of the card, though, would be very similar to a debit card. Like fiat-backed credit/debit cards, the card could contain an account number. Upon swiping the card, the device would send a request to a server owned by the bank/credit card company requesting funds, authorized by the account holder. The company then sends the funds.
It strikes me that a lot of the users of Bitcoin use Bitcoin largely because they are against financial institutions or government issued money; however, most of the world is quite happy to not have to be responsible for the safety of all of their own money, which is why banks exist--I certainly don't keep my money there because of the <1% annual interest it seems like I'm getting. A decentralized currency can coexist with financial institutions. To me the biggest strength of Bitcoin is that all of its features seem to be optional: you can be nearly anonymous, or you can decide not to be. You can set up a transaction to be irreversible, or you can use escrow to allow the transaction to be "undone," in effect. Advanced users who care can keep all of their coins in a private wallet without any trouble, but average users (by which I mean, largely, people who don't use bitcoin yet) can use banks and the like. People have mostly adopted Bitcoin so far either because it's "cool," as an investment, or because they value its features more than fiat money. To spread to people who don't want to invest in bitcoin and aren't tech savvy enough to understand it and find it cool, Bitcoin must develop features that make it better than fiat currencies for day-to-day transactions in the eyes of the everyman.