Tacrolimus is a relative new drug to the veterinary world. It comes from a class of medications called "calcineurin inhibitors," and it is used most frequent for treating keratoconjunctivitis sicca (also known as KCS or dry-eye). Less commonly this medicine is used topically to treat for allergies (atopy) and for some of the autoimmune skin diseases (discoid lupus erythematosus, pemphigus erythematosus, etc.). In human medicine this medication is used orally for similar conditions at massively higher dosages.

The link between cancer and Tacrolimus was observed in humans following organ transplantation, who were taking very high dosages orally. This effect has been reproduced in mice, using a topical (skin) application model, but again at extremely high dosages. The issue appears to be related to how much of the mediation is absorbed systemically. Using Tacrolimus topically in the eye, there is no systemic absorption. Using the medication topically on the skin at normal application levels, there is no demonstrable systemic absorption. Using the medication topically on the skin at 25 times the normal application level the drug can be detected systemically and there would be a small increased risk of cancer.
Philosophically all medications pose a certain amount of risk and should not be used unless the risk (and potential side effects) are warranted. Since your dog has KCS (dry-eye), he is at risk of chronic discomfort, inflammation, secondary eye infections, and ultimately severe changes to the corneas and/or vision loss. In mild cases you can treat with artificial tears (available over-the-counter), which are available in both a cream form and a liquid (eyedrop) formulation. If these are not sufficient (and usually they are not) then your choices are Cyclosporine Ophthalmic or Tacrolimus. Cyclosporine used to be widely available as a compounded medication and was relatively affordable. Recently it has been almost impossible to find it in this form and even the big national compounding pharmacies have stopped making it. There is still a commercial form of Cyclosporine available (a cream called Optimmune) which is very good, but also relatively expensive. If you are still concerned about using Tacrolimus you could ask your vet about Optimmune. Personally I am very comfortable with the minimal (non-existant?) risk of cancer that the ophthalmic form of his medication creates. Over the past six months I have transitioned all of my patients with dry-eye to either Tacrolimus or Optimmune. There has been at least one study to show that Tacrolimus is at least as effective as Cyclosporine, and may also be effective in those patients who are resistant to the effects of Cyclosporine.

This is a more in-depth answer to your question (from "Pimecrolimus & Tacrolimus - Not a Cancer Risk," Drs. Mark Rishniw, Douglas Kemp, GiGi S. Davidson, VIN):
What evidence is there of carcinogenesis?
Tacrolimus has been shown to increase risk of neoplasia in humans taking the drug orally to prevent transplant rejection. Animal models with pimecrolimus and tacrolimus, administered orally, also showed increased risk of neoplasia.
Dermal application of tacrolimus or pimecrolimus in mice showed a dose-dependent carcinogenic effect. However, the drugs were applied in an ethanol base, and at doses that were 26 and 47 times the maximum recommended human doses (based on area-under-the-curve comparisons).
Following systemic exposure of monkeys with lymphocryptovirus to oral pimecrolimus at 31 times the maximum recommended human dose for 39 weeks immunosuppressive-related lymphoproliferative disorder was observed.
What is the evidence that they are safe?
Most of the data demonstrating carcinogenic risk has been performed in animal models using greatly excessive doses of drug, often administered orally.
Humans using therapeutic doses of these drugs topically generally had undetectable serum concentrations of drug, and tests of immune function in human patients receiving topical therapy with these drugs showed no evidence of immunosuppression.
Data from Novartis demonstrated that eight malignancies including one colon carcinoma and one squamous cell carcinoma occurred in the clinical trial patients and six malignancies occurred in patients identified from postmarketing surveillance spontaneous reports. Independent experts reviewed the available evidence and concluded that there is no evidence of a causal link between the use of pimecrolimus and the occurrence of the malignancy, based on the type, timing and site of the malignancy.
Worldwide exposure to pimecrolimus is estimated at 814,138 person-years, 520,000 person-years being in the under 10-year age group. Five million individuals have been exposed to pimecrolimus, over 19,000 of these in clinical trials. The average patient uses 75 g per year and treats for 45 days of the year. American sales of pimecrolimus amount to 6,780,000, 70% of these being new prescriptions, and for tacrolimus 2,797,000. There has been worldwide clinical trial exposure to topical tacrolimus in 19,000 adults and 7600 children. A study of 9813 patients during the U.S. clinical development of tacrolimus included 1718 person-years of exposure to tacrolimus in adults aged over 40 years. Patients were followed up for up to 3·5 years and 13 developed nonmelanoma skin cancer (eight basal cell carcinoma and five squamous cell carcinoma). The estimated incidence in these patients was between 361 and 1217 per 100,000. This compared with 533 per 100,000 in a male reference population not exposed to tacrolimus.
The lymphoma rate for tacrolimus treatment is 0·65 per 100,000, compared with an expected 22 per 100,000. Therefore, the incidence of lymphoma, particularly non-Hodgkin, is below that expected by chance in the normal population on the basis of person-years of exposure.
Non-melanoma skin cancer rates in patients on tacrolimus were no different from controls.
This data are strongly supportive of the hypothesis that tacrolimus and pimecrolimus, given topically at recommended doses, do not cause neoplasia in humans. However, as with any strongly immunosuppressive drug, caregivers should be warned to wear gloves or wash hands after handling these drugs.
What conditions can I use these drugs for?
The most common uses of tacrolimus or pimecrolimus in veterinary medicine are for atopy, keratoconjunctivitis sicca, discoid lupus erythematosus and pemphigus erythematosus. It is important to note that all veterinary applications of tacrolimus are topical (either by application to the skin or the eyes) at this time. Systemic use of tacrolimus has proven to be nephrotoxic in dogs and has not been sufficiently evaluated for systemic use in cats.
The commercially available ointment preparations (Protopic®) are not suitable for use by the ophthalmic route as they contain propylene carbonate which is a known ocular toxin. Tacrolimus for ophthalmic use will need to be prepared by a compounding pharmacy from sources other than the commercially available topical ointments.