Transcriptome assemblers that either perform de novo assembly of transcripts from sequence reads or do so with the help of a reference assembly (and perhaps even guided by known transcript annotations). These include: Cufflinks, Scripture, Trinity, Trans-ABySS, GRIT, etc. Of these, Cufflinks is probably the easiest to use while Trinity and Trans ABySS seem to yield impressive results in the hands of certain groups (particularly those that developed them...).
There are also many tools that are usually considered for straight differential expression but if run the right way might still yield results informative to alternative expression of isoforms. These include: edgeR, DEseq, htSeq, DEGseq, sSeq, etc.
Note that placing each tool in one of three categories is an over-simplification. Some span across the three activities and some are components of a workflow generated by a single research group. Overall the area is a bit of a wild west. More tools are being developed constantly and you will find aspects of all of them that leave you wanting something better. The problem is not a simple one and is an area of active research.
I just pushed an update of my R package IsoformSwitchAnalyzeR to Bioconductor which introduces a module for alternative splicing.
For individual splice sites the already suggested tools might be better - but for a genome wide analysis of splicing it is very convenient to frame it as a comparison of isoforms that are switching since it allows for easy interpretation and statistical analysis. For examples of what it can do see the alternative splicing part of the vignette here.
As a bonus IsoformSwitchAnalyzeR also allows you to identify and analyze isoform switches with predicted functional consequences (both for individual genes and genome wide) meaning it will help you figure out what result of the identified the alternative splicing is.
Very informative post, I just wonder if anyone has done alternative splicing analysis with nextera kit derived library, which has a broad size distributed fragments. Would that diverse library affect the algorithms? Any recommendation for this kind of library analysis?