It depends on the receiver. The cheaper ones don't do as well with multipath, but the better ones do.
I was having problems getting ANALOG stations on a nice TV set that someone had. Out of maybe 9 receivable channels (this was in the city, North Miami Beach to be exact), a nice set of rabbit ears netted 2 "very good" channels, two more just watchable, and the rest were terrible (this was the ANALOG reception). Terrible multipath problems, snowy pictures, just terrible.
In desparation, I got the family a digital converter, the Zenith DTT901. Hooked it up to the TV's better inputs (rca/phono plugs in the back), and hooked up the rabbit ears to it. Had it "search" for digital channels, and it found about 23. The picture quality? For most channels it was EXCELLENT. Some channels you could tell were transmitted with more compression, so they were softer. As long as you got decent signal reception, you got a perfect picture with few if any episodes of pixelation.
So my experience has been good.
Most reviewers I checked who seem to have some experience with these things recommend this unit as the best one for people who may have difficult reception. I picked one up today at Radio Shack and it does the job using a plain rabbit ears.
One station (the NBC affiliate) has just barely enough signal and requires very careful adjustment of the antenna. (The built-in signal level meter helps in this regard.) I can see a lot of people losing stations like this when and if the changeover occurs.