So I've got a list of chromosome segments amplified and deleted by sample with the chromosome, start and end co-ordinates. How can I, using R, get hold of identifiers for all the genes that fall within those segments?
Store your amplified/deleted segments in a GRanges object (from the GenomicRanges package) named gr. You can annotate each range in this object with the sampleID it comes from, if this is necessary.
Load up the appropriate TranscriptDb object (GenomicFeatures package) for your organism and reference, or create your own from a set of annotations you care about (read the vignette for this package to learn how to do so).
Get the relevant features you want out of your txdb objects, and subsetByOverlaps(features, gr) .
More concretely, assuming your working in human:
tx <- transcripts(TxDb.Hsapiens.UCSC.hg19.knownGene)
interesting <- subsetByOverlaps(tx, gr)
Now interesting has all of the transcripts that overlap (in any way) with the segments in gr. Read through the documentation available for GenomicRanges (and likely IRanges) to tune how you want to consider overlaps, or how to use the lower level findOverlaps methods to better tune the results/output from these queries.