How many times did terrestrial life emerge from the ocean?
I doubt we know the precise number, or even anywhere near it. But there are several well-supported theorised colonisations which might interest you and help to build up a picture of just how common it was for life to transition to land. We can also use known facts about when different evolutionary lineages diverged, along with knowledge about the earlier colonisations of land, to work some events out for ourselves. I've done it here for broad taxonomic clades at different scales - if interested you could do the same thing again for lower sub-clades.

As you rightly point out, there must have been at least one colonisation event for each lineage present on land which diverged from other land-present lineages before the colonisation of land. Using the evidence and reasoning I give below, at the very least, the following 9 independent colonisations occurred: 


bacteria
cyanobacteria
archaea
protists
fungi
algae
plants
nematodes 
arthropods
vertebrates


Bacterial and archaean colonisation
The first evidence of life on land seems to originate from 2.6 (Watanabe et al., 2000) to 3.1 (Battistuzzi et al., 2004) billion years ago. Since molecular evidence points to bacteria and archaea diverging between 3.2-3.8 billion years ago (Feng et al.,1997 - a classic paper), and since both bacteria and archaea are found on land (e.g. Taketani &amp; Tsai, 2010), they must have colonised land independently. I would suggest there would have been many different bacterial colonisations, too. One at least is certain - cyanobacteria must have colonised independently from some other forms, since they evolved after the first bacterial colonisation (Tomitani et al., 2006), and are now found on land, e.g. in lichens.

Protistan, fungal, algal, plant and animal colonisation
Protists are a polyphyletic group of simple eukaryotes, and since fungal divergence from them (Wang et al., 1999 - another classic) predates fungal emergence from the ocean (Taylor &amp; Osborn, 1996), they must have emerged separately. Then, since plants and fungi diverged whilst fungi were still in the ocean (Wang et al., 1999), plants must have colonised separately. Actually, it has been explicitly discovered in various ways (e.g. molecular clock methods, Heckman et al., 2001) that plants must have left the ocean separately to fungi, but probably relied upon them to be able to do it (Brundrett, 2002 - see note at bottom about this paper). Next, simple animals... Arthropods colonised the land independently (Pisani et al, 2004), and since nematodes diverged before arthropods (Wang et al., 1999), they too must have independently found land. Then, lumbering along at the end, came the tetrapods (Long &amp; Gordon, 2004).

Note about the Brundrett paper: it has OVER 300 REFERENCES! That guy must have been hoping for some sort of prize.

References


 Battistuzzi FU, Feijao A, Hedges SB. 2004. A genomic timescale of prokaryote evolution: insights into the origin of methanogenesis, phototrophy, and the colonization of land. BMC Evol Biol 4: 44.
 Brundrett MC. 2002. Coevolution of roots and mycorrhizas of land plants. New Phytologist 154: 275–304.
Feng D-F, Cho G, Doolittle RF. 1997. Determining divergence times with a protein clock: Update and reevaluation. Proceedings of the National Academy of Sciences 94: 13028 –13033.
 Heckman DS, Geiser DM, Eidell BR, Stauffer RL, Kardos NL, Hedges SB. 2001. Molecular Evidence for the Early Colonization of Land by Fungi and Plants. Science 293: 1129 –1133.
Long JA, Gordon MS. 2004. The Greatest Step in Vertebrate History: A Paleobiological Review of the Fish‐Tetrapod Transition. Physiological and Biochemical Zoology 77: 700–719.
 Pisani D, Poling LL, Lyons-Weiler M, Hedges SB. 2004. The colonization of land by animals: molecular phylogeny and divergence times among arthropods. BMC Biol 2: 1.
 Taketani RG, Tsai SM. 2010. The influence of different land uses on the structure of archaeal communities in Amazonian anthrosols based on 16S rRNA and amoA genes. Microb Ecol 59: 734–743.
 Taylor TN, Osborn JM. 1996. The importance of fungi in shaping the paleoecosystem. Review of Palaeobotany and Palynology 90: 249–262.
Wang DY, Kumar S, Hedges SB. 1999. Divergence time estimates for the early history of animal phyla and the origin of plants, animals and fungi. Proc Biol Sci 266: 163–171.
 Watanabe Y, Martini JEJ, Ohmoto H. 2000. Geochemical evidence for terrestrial ecosystems 2.6 billion years ago. Nature 408: 574–578.