See also this news article: http://www.xconomy.com/national/2013/04/29/six-reasons-why-illumina-has-nothing-to-fear-from-thermolife-merger/

So does Illumina have any real competition on the sequencing market?

Iontorrent doesn't seem to make true it's promises and it lacks the quality (al least for homo polymer section of reads) against Illumina. And Illumina has the Mi-Seq to compete with it.

PacBio is very expensive and only useful in a niche market where you really need long single reads, for example complex genome denovo assemblies.

SOLID is lagging behind in read length, color space produces lot's of headaches for analysis, and there is a lack of community tools to handle the data.

454 is not developed / used anymore?

Oxford nanopore and others are still very experimental and not ready for "production" use.

An advantage of the dominance of Illumina is that everybody is compatible which each other, like all the Microsoft Windows / Office users, but this also means like in the Microsoft top days that they can do and ask whatever they want from their customers.