Why are there splice variants within the same organism? What might contribute to the need for the feature?
The reason is very simply to provide enough variation in a limited sized genome to produce the repertoire of proteins produced by the cells of multicellular organisms. It is also a matter of efficiency and reduced energy consumption.

Consider that on average there are about 100,000 unique protein types being produced in a human cell [1], but the human genome is estimated to contain only 19,042 protein coding genes [2], then the cell needs some way to vary that limited instruction set.

Also remember that differentiated cell types express certain genes but not others, and produce different proteins that other cells do. So that implies that there are more than 100,000 different types of human proteins, and far fewer than 19,042 genes being expressed in any one cell at the same time.

So without splice variants, our genomes would either need to be far larger than the approximately 3 billion base pairs it is already or our repertoire of proteins would be significantly less. We would also have a lot of redundancy, as many common exons would have to be repeated over an over again. That would require a lot more energy for DNA synthesis, and nucleic acid synthesis, etc. The process would become inefficient rather quickly and would likely make complex multicellular animal life untenable.

There is a bit of an error in your question. Splice variants are identified by the mRNAs that are produced, and exons are defined by the sequence that is in the mature mRNA. Introns are, by definition spliced out of the pre-mRNA, meaning that splice variants are not "produced by different combinations of introns and exons." Splice variants will only consist of different combinations of exons. The only time an intron would be found in a mature mRNA is if a splice site is mutated and it is no longer recognized by the spliceosome, so it leaves the intron in incorrectly. This will generally result in a non functional protein.

EDIT


  The collection of components required to carry out the intricate processes involved in generating and maintaining a living, breathing and, sometimes, thinking organism is staggeringly complex. Where do all of the parts come from? Early estimates stated that about 100,000 genes would be required to make up a mammal; however, the actual number is less than one-quarter of that, barely four times the number of genes in budding yeast. It is now clear that the 'missing' information is in large part provided by alternative splicing, the process by which multiple different functional messenger RNAs, and therefore proteins, can be synthesized from a single gene.


-Expansion of the eukaryotic proteome by alternative splicing: Nilsen and Graveley


  Alternative splicing of pre‐messenger ribonucleic acid (pre‐mRNA) allows the generation of different mRNAs from the same gene. Evolution of alternative splicing affecting translated regions of mRNAs permits the synthesis of different proteins from a single gene, significantly increasing the diversity of the protein repertoire.


-Patthy, László(Apr 2008) Alternative Splicing: Evolution. In: eLS. John Wiley &amp; Sons Ltd, Chichester.

Also while I am not one to accept a Nobel Prize at face value, they are usually awarded when the field accepts the explanation of the hypothesis. The 1993 Nobel Prize in Physiology and Medicine was awarded to Richard J. Roberts and Phillip A. Sharp "for their discovery of 'split genes'."