As /u/l33t_sas suggested, the Pacific world was very extensively connected in the pre-contact and early contact eras. There's been a wellspring of work on that topic in the wake of Epeli Hau'ofa's essay "Our Sea of Islands", which was published in 1993. Hau'ofa argues that the image of Pacific islands as small, remote, and isolated is one created and fostered by colonialism, and that Pacific islands are more properly understood as part of a large Pacific world and deeply interconnected.

There have been some wonderful theoretically-oriented pieces like Joakim Peter's "Chuukese travelers and the idea of horizon," which seeks to connect Islander's travel in the past with contemporary movement and to examine the meaning of that movement. Geographers like Lola Bautista have done more on-the-ground fieldwork to investigate the ways in which islanders continue to travel, the pathways through which they move, the relationship between contemporary and historical travel, and the meaning of that travel.

But historians have been involved in this work also. Kealani Cook just completed a dissertation at the University of Michigan called "Kahiki: Native Hawaiian Relationships With Other Pacific Islanders, 1850-1915" which, as you might imagine, seeks to connect Hawai'i with a broader Pacific world. Alice Somerville's Once Were Pacific does something a bit similar, although it's more focused on contemporary relationships among Maori and other Pacific Islanders (in New Zealand).

Of course there's also the literature on navigation, within which I particularly like Paul D'Arcy's People of the Sea. If you're interested in the mechanics of navigation, that's not a bad place to go -- and it paints a pretty legible picture of which islands would have been more connected and for what reasons. For example, within Micronesia, high volcanic islands like Pohnpei or Kosrae would have had somewhat less motivation to foster cultures of long-distance voyaging because those islands tended to be fertile enough to provide residents with anything they needed. The same is true for Hawai'i. Voyaging existed in all three of those places, and very long distance voyages certainly took place from time to time, but most trips tended to be short or medium range. In the Central Caroline Islands, however, since most people lived on low coral atolls that were more susceptible to droughts or storms, voyaging represented an insurance policy of sorts -- so Central Carolinians paid a tribute to a traditional leader on the high island of Yap to have an extra layer of protection in times of crisis. A similar situation obtained in the Marshall Islands, except that there was no central high island. Instead, Marshallese atolls were deeply connected with one another -- to the extent that many Marshallese claimed (and claim) multiple atolls as their homeland.

I don't meant to imply that voyaging is all in the past. It isn't, and many islands maintain a thriving culture of navigation. But it's also true that Pacific Islander interconnectedness and mutual dependency never ended. Pathways of connection were interrupted or reshaped by colonialism and the boundaries it erected in the ocean, but as Hau'ofa argued, Islanders have long "made nonsense" of those boundaries by continuing to move across them. Pacific Island voyaging has been transmuted into other forms, in other words.

Prehistory in the Pacific had extensive contact, even between distant islands and this can be observed in the vocabulary of Micronesian and Polynesian languages. Rehg and Bender (1990) identify 172 loanwords in Mokilese (Mokil is a small atoll in Pohnpei state) from Marshallese (the Marshall Islands are over 500 miles east of Mokil). They also note some historic visits to Mokil and other parts of Micronesia (p. 4):

1856: Five canoes, with 100 Ebon men, women, children blown off course while travelling from northern to southern Marshalls. . After 15 days drifted to Kusaie arriving in April. Built a new canoe and with four canoes in all departed Aug. 18, taking with them other Marshallese who had been living at Kusaie. (175a)

Thirty people in two canoes, in addition [to those mentioned above] and part of the same party, having become separated at sea, reached Mokil.

A boat was swept from Ralik to Kusaie and a few days later another boat to Mokil; the crew succeeded in getting home.

1857: Thirty Ralik people were on Mokil; they had come there 18 months earlier.

1859 (?) Two canoes from the Marshalls drifted to McAskyl's (Pingelap), two at Wellington's (Mokil), five at Strong's (Kusaie), March 5th and 6th.

July, 1860: Two canoes, with 40 Marshallese men, women and children, arrived at Kusaie from Mokil, having stopped at Pingelap en route, after five days' journey. Two weeks later set out for the Marshalls. (Possibly were the same party mentioned under No. 176, Ebon to Mokil, now returning home after four years.)

1862: A party of Marshallese "this year beat back to their home from Wellington (Mokil), which is nearly 600 miles to the west, and that without any of the appliances the educated navigator would consider indispensable." (169c)

1875 Two canoes from Majuro, people arrived Kapingamarangi exhausted and starving; they came from Majuro via Mokil. (184b)

People in Kiribati also have oral histories documenting extensive contact with Polynesia. Nauruan contains several borrowings from Kiribati, Marshallese and Polynesian languages. The Yapese got their famous stone money from Palau (imagine carrying those back in a canoe!). Just think that the Marshall Islands and Kiribati, despite both being archipelagos spread out over several 100s of miles (Kiribati is over 1000 miles from end to end) and having been settled over 2000 years ago nevertheless still each just have one language (though with considerable internal variation). Or in Polynesia, the Tuamotu archipelago, spread over an area the size of western Europe, again only speaking one language (with two minor exceptions). Think of the level of contact that necessarily requires. Indeed Marck (1986) has proposed "the overnight voyaging hypothesis" for Micronesia which holds that:

If two islands are separated by a voyaging distance involving a single night at sea or less in traditional craft, their dialects will be mutually intelligible.

(note that this hypothesis is specifically for Micronesia. It might also work well for Polynesia, but it certainly doesn't for Melanesia where you can have several islands very close to each other with non mutually intelligible dialects)

It turns out that this hypothesis is mostly supported (with some minor exceptions). But this has to give you an idea of how frequent travel must have taken place. After all, it doesn't matter how close the islands are, if people don't actually make the trip and talk to one another, the dialects are not going to stay mutually intelligible!

In Melanesia, there are well-documented and studied complex inter-island trading networks such as the Kula Ring in the Milne Bay province of PNG and the Hiri Trade Cycle.

Okay I think I've reached the part where I just chuck references your way. These are mainly linguistic ones, but there's a whole bunch of archaeological and anthropological stuff out there that I'm just not familiar with.

Leach, J., & Leach, E. (1983). The Kula: New Perspectives on Massim Exchange. New York: Cambridge University Press.
Marck, J. C. (1986). Micronesian dialects and the overnight voyage. Journal of the Polynesian Society, 95, 253–258.
Oram, N. D. (1982). Pots for Sago: the Hiri trading network. In Thomas E Dutton (Ed.), The Hiri in History (pp. 1–33). Canberra: Developmental Studies Institute.
Pawley, A. (2007). Why do Polynesian island groups have one language and Melanesian island groups have many? Patters of interaction and diversification in the Austronesian colonization of Remote Oceania. Presented at the Workshop on Migration, Ile de Porquerolles.
Rehg, K. L. (1995). The Significance of Linguistic Interaction Spheres in Reconstructing Micronesian Prehistory. Oceanic Linguistics, 34(2), 305–326.
Rehg, K. L., & Bender, B. W. (1990). Lexical Transfer from Marshallese to Mokilese: A case of intra-Micronesian borrowing. Oceanic Linguistics, 29(1), 1–26.
Rhoads, J. (1982). Prehistoric Papuan Exchange Systems: The Hiri and its Antecedents. The Hiri in History. Further Aspects of Long Distance Motu Trade in Central Papua (pp. 131–150). Canberra: Australian National University.