Two types of dust disks around white dwarfs (WDs) have been reported: small dust disks around cool metal-rich WDs consisting of tidally disrupted asteroids and a large dust disk around the hot central WD of the Helix planetary nebula (PN) possibly produced by collisions among Kuiper-Belt-like objects. To search for more dust disks of the latter type, we have conducted a Spitzer MIPS 24 μm survey of 71 hot WDs or pre-WDs, among which 35 are central stars of PNe (CSPNs). Nine of these evolved stars are detected and their 24 μm flux densities are at least two orders of magnitude higher than their expected photospheric emission. Considering the bias against the detection of distant objects, the 24 μm detection rate for the sample is ≳15%. It is striking that seven, or 20%, of the WD and pre-WDs in known PNe exhibit 24 μm excesses, while two, or 5%-6%, of the WDs not in PNe show 24 μm excesses and they have the lowest 24 μm flux densities. We have obtained follow-up Spitzer Infrared Spectrograph spectra for five objects. Four show clear continuum emission at 24 μm, and one is overwhelmed by a bright neighboring star but still shows a hint of continuum emission. In the cases of WD0950+139 and CSPN K1-22, a late-type companion is present, making it difficult to determine whether the excess 24 μm emission is associated with the WD or its red companion. High-resolution images in the mid-infrared are needed to establish unambiguously the stars responsible for the 24 μm excesses.