Yes, and I want (and expect) to see +2, +3, +4, and +5 weapons. The key, as many have said, is somehow avoiding "magic item reliance."
In some sense the issue of +X weapons is key to 5E design because it is an example of how 5E is trying to take an approach of "Let's have our cake and eat it too," which I applaud but is rather difficult to actualize. How to have +X weapons that actually make a difference but, at the same time, don't enable magic item reliance?
One obvious solution (such as it is) would be to not allow item bonuses to stack with certain kind of feat-related or specialization bonuses, but this is one of those "gamist" rules that erodes a sense of realism. Why shouldn't a magic weapon be easier to hit with?
Another possibility that comes to mind is something that I've been playing with in my own game. What if bonuses only "un-pack" when the PC gets to a certain level? Let's say that a PC can only use a bonus at a rate of something like +1/5 levels; this means that a +5 sword in the hands of a 2nd level character would be a +1 sword; they simply don't have the experience and "magic resonance" to unlock the full power of the weapon. So it would be something like this:
Level: Bonus
1-5: +1
6-10: +2
11-15: +3
16-20: +4
21-25: +5
26-30: +6
31+: +7
Or something like that. That way there's a mechanism to keep the math from getting out of control, but the bonuses still make a meaningful--but not absolutely necessary--difference, something like 10-20% of the total attack bonus, I would imagine.
Another cool thing about this approach is that Epic level weapons, like Excalibur, could be +6 weapons, and immortal weapons, like Mjolnir, could be +7 weapons - but both only usable at that power level by PCs of the required level.
This approach also encourages less of a "magic item treadmill." One of the irritating things about 4E is that you find a magic weapon and within a few levels you've outgrown it. What if that +1 longsword that you found at 2nd level is actually a legendary +4 longsword with unlocked powers and history? This allows a PC to have an iconic magic item over many levels, and really grow into it.
Now of course this doesn't fully negate magic item reliance, but it at least balances things out a bit and avoids level-inappropriate magic items ("too powerful too soon").
On the other hand, bonuses to hit could be done away with and replaced with something interesting. Start with bonuses to damage, but then add something that effectively adds a bonus to attack, like a magic weapon that allows re-rolls of Natural 1s and 2s or a bonus d4 "wild die" added to your attack roll. The point being for some sort of mechanism that says "This helps, but isn't absolutely necessary."