Let DC Vote
At a bare minimum, DC needs a Representative with status equal to that of the other Reps. The Senate is a bit tougher of a question, since I think the two-Senators-per-state system is wrong (I'd rather change the Senate to nationwide Proportional Representation, in which DC would of course vote). So I'm undecided between giving DC two Senators of its own, or the alternative (and more politically feasible) suggestion of letting it vote in the Maryland Senate elections. Indeed, I would be happy to retrocede DC back into Maryland, just like Arlington long ago returned to Virginia.
There are two basic arguments advanced against giving DC representation: the "vested interest" argument and the "non-favoritism" argument. I don't think either holds water, particularly when matched up against the competing claims of political equality for all citizens.
The "vested interest" argument says that DC residents are all federal employees, so if they were able to vote they'd vote for higher taxes and bigger government to benefit themselves at the expense of people working in the private sector. This argument is wrong at three levels -- principle, sociological, and efficiency. At the level of principle, it fails because the right to have a say in how a community (such as the nation) is run flows from membership in that community, as defined by someone's actual entanglement with the lives and fortunes of others*. It's not contingent upon whether you will vote the right way.
On the sociological level, the vested interest argument fails because it assumes that federal employees are uniquely inclined and able to vote in their self-interest at the expense of others.
But even if we accept the vested interest argument at the level of principle and sociology, it fails at the level of efficiency because it makes an unjustified equation between "federal employee" and "DC resident." If you want to disenfranchise federal employees, then disenfranchise federal employees. While the federal government is the biggest employer in DC, it only provides 27% of the jobs, so there are plenty of people in DC -- from Georgetown professors to taxi drivers -- who do not work for the feds. They shouldn't lose the vote based on their neighbors' jobs. What's more, there are loads of federal employees who don't live in DC. The Washington metro area has expanded well beyond the boundaries of the District. Why should a Commerce Department number-cruncher get representation in Congress just because she happens to live across the border in Montgomery County or Alexandria? And of course there are all the federal employees in regional offices scattered across the country. A Park Ranger at Yellowstone gets two Senators and a Representative, while his colleague at the Smithsonian gets nothing. I won't even go into the millions of Americans who are effectively federal employees because they work for defense contractors, or agribusinesses that benefit from the federal push for ethanol, or are otherwise beneficiaries of pork.
The "non-favoritism" argument refers back to the original purpose of creating the District of Columbia, rather than putting our capital in Philadelphia or New York. Some people simply assert that DC wasn't supposed to be in a state, period. But since there's no reason to accept that as a fundamental axiom, we have to look at the reasons why DC shouldn't be in a state.
I think the real reson DC was created from scratch is to avoid showing favoritism to already-existing states and cities. That's a very worthy goal, especially since the union was so fragile at the time of DC's founding. But giving the current residents of DC the vote wouldn't undermine that goal. The White House isn't going to up and move to Philly if we give Elanor Holmes Norton some real power.
A more updated version of the non-favoritism argument is that if the people of DC had any power, they would meddle in the federal government's business, either accidentally or maliciously impairing its ability to do its job and be fair to all Americans.
But as it stands today, the big problem is just the opposite -- DC has no power to defend itself against the meddling of the federal government. The city can't even cast a single "nay" vote when the legislators from the remainder of the country gang up to overrule DC citizens' democratically-chosen laws. One prominent example is the feds' resistance to a commuter tax. So instead of being able to recoup some money from the rich suburbanites who work in the city and use its services, DC has to jack up the taxes and fees on its own disproportionately poor and minority population. Some reasonable limits on the city's jurisdiction over federal property (with a high burden of proof on the federal government to show it had been harmed) is a much better solution than the disenfranchisement of an entire city.
Empirical evidence is helpful here too. The governments of the UK and France seem to be doing just fine without taking the vote away from the citizens of London and Paris. State governments likewise haven't needed to kick the people of Harrisburg or Albany out of their legislatures. And the federal government has plenty of offices outside of the bounds of DC (including the Pentagon) which haven't been crippled by meddling voters.
*I'm happy to follow this principle to the logical conclusion that immigrants should be able to vote.