Acid-resistance residues were prepared for eighteen meteorites from seven chondrite classes, using improved procedures designed to minimize loss of presolar grains. Noble gases were measured by stepped pyrolysis, and the abundances of five exotic noble-gas components were used to determine abundances of diamond, SiC, and graphite. Diamond separates were prepared to check diamond abundances determined from noble gases. Diamond and SiC were found in unmetamorphosed members of all seven chondrite classes and evidence for graphite was found in Orgueil (CI) and LL3.0-3.1 chondrites. Our data and noble-gas and stable-isotope data in the literature show that presolar grains were incorporated into all chondrite classes. The grains are sited in the fine-grained matrix, and their abundances within the matrix reflect mainly the degree of metamorphism suffered by the host meteorite. The pattern of metamorphic destruction differs from class to class. In unequilibrated ordinary chondrites (UOCs), graphite is most easily destroyed, followed by SiC and then diamond. No presolar grains remain in UOCs of petrologic type > 3.8, whose matrices have been completely recrystallized. In EH chondrites, diamond and SiC survive much more severe metamorphism than in UOCs, with SiC apparently more stable than diamond. Presolar graphite was not detected. In CV3 and CO3 chondrites, diamond appears to be more stable than SiC and graphite again is missing. Inferred premetamorphic diamond abundances (matrix normalized) vary by a factor of approximately 2.2 between classes, with EH, CV, and CO chondrites having higher initial abundances than Orgueil. Similar diamond/SiC ratios are observed in most classes and differences in the ratio can be tied to secondary processing, suggesting that all chondrite classes sampled the same solar-system-wide reservoir of presolar grains. Differences in initial abundances between classes appear to correlate with chemical and physical properties of the most meteorites. These bulk properties and variations in presolar-grain abundances both may be the result of thermal processing of presolar dust in the accretion disk.