The simple solution to this is to clear the room between panels of course, but not only does that take extra time, it also kind of screws over anyone who actually was interested in seeing two of the panels in a row. Of course sometimes life just sucks. Sometimes there are two panels you want to see at the exact same time. Sometimes there are two popular panels back to back in different rooms, and if you stay all, or even partway, through the first one you won't be able to get in line for the second one early enough to get in. What this solution would do is just make it so that every panel was in a "different room" from every other panel. You'd just have to plan around which panels you _really_ wanted to see, and which you'd like to get in if there's room but could live without.
coraa suggesting ticketing as another possible solution, at least for the really popular events, which is a pretty good idea, but it immediately brought to mind Ax's solution to the really big events, you can wait in a long line for a couple hours to get free tickets, or you can pay $20 upfront to get "better" tickets and skip the waiting in line. ("Better" meaning closer to the front, which may or may not actually be better, depending on how loud the speakers are turned up =P)
So here's my totally impractical without ubiquitous computing solution. You have an auction for tickets for all the popular panels, or possible every panel at the con. The auction starts a couple hours before the panel, let's say three hours before seating starts. At the end the top X bidders are assigned the X tickets, in order of their bids. You don't want lots of sniping going on during the last few minutes, so you add artificial amounts to every bid as time progresses. Perhaps about five cents a minute, so by the end of the three hours an initial bid of one cent would be the equivalent of $9.01. The bidder would still pay just one cent of course, the extra money is a "bonus" to encourage early bidding, since someone who wanted to snipe that person at the last minute would have to pay $9.02 to beat them.
In cases of ties i'm not sure if it would be fair to give preference to the person who put in the last bid (since we already front-loaded the benefit for early bidders) or the person who put in the first bid (since they'd lose to most accrued advantage if they have to re-bid.)
When the auction ends all the bids are compared and tickets are issued in order. In default this would be from front to back, but it would probably be possible to set preferences ("aisle seat closest to the front when my ticket comes up" or such.)
This would theoretically eliminate the need for huge lines and allow people to go to multiple panels one right after the other (again, assuming the ubiquitous computing necessary to make the idea feasible) but it would definitely prejudice things towards those with more extra money than free time. The most important thing to do would be to try and insure there wasn't huge amounts of inflation. As long as the majority of the people are getting in for less than $1 of real currency it's probably not a big problem. If people have to start spending significant amounts of money just to get into the rear of the room for a panel at a con they're already paying to attend they're going to be justifiably upset.
Assuming the con management was responsible they could lower the con fees proportional to the amount they take in on ticket sales, but that's wouldn't be a psychologically immediate benefit. They could also give every attendee a certain amount of virtual dollars to be spent on bidding for panels, which would inevitable result in a certain amount of inflation, but would equalize the field a little bit. Or of course they could just use this strategy for about half the seats and leave the other half for whoever was willing to wait in line. However that might actually lead to inflation as well. Not only would the supply be reduced, but there might be a different psychological responses to "oh no, i got outbid, now i need to pay more or i can't go," and "oh no, i got outbid, now i need to pay more or else i'll have to get in line/or else some other dude will get in for free when i can't."
Anyways, i'd be interested in the results of such a system, but unfortunately it's not even going to be technically feasible for several years at _least,_ and might not be considered acceptable in a PR sense even after that.