Best overall, especially for checking SNPs across multiple samples: IGV. The major problem to me is IGV does not display inserted sequences (still true?).
Most beautiful: Tablet. It supports more formats, but does not provide enough information for eye-checking variant calls. I always find IGV to be more convenient for my tasks.
For ChIP-seq: SeqMonk. Heard good things about it; never used.
Occasionally handy: samtools' tview (when over slow network or for quick check). One of the few viewers that display inserted sequences (what else besides gap5?). But most users would prefer IGV instead.
The only assembly editor: gap5. You need to convert BAM to the gap5 format first.
Others: BamView (limited functionality), MagicViewer (not always working) and Gambit (not so mature as others). There are a few more but I forgot the names.
IGV:
Jeremy Leipzig has written a nice review on NGS viewers which may help answer some of your questions: http://jermdemo.blogspot.com/2010/08/ngs-viewers-reviewed.html
Awesome list of viewers: https://github.com/cmdcolin/awesome-genome-visualization
Here is a link to my review of BAM/SAM viewers in context of RNA-seq and fusion genes discovery:
Visualizing RNA-seq alignments with fusions: is there anything better than IGV?
Well, since this question came back to the top here's my answer: for BAM and other genomic formats I use my own tool ASCIIGenome
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Is it possible for SAMtools tview to omit showing a mapped read for whatever reason?