Are there any other mammal species where males take care of their offspring like humans do?

Biologists call biparental those species in which the male invest a great effort in raising his offspring, understanding that the female always does her share.

As I see it, this label, biparenting, is somehow flawed since in some (very strange) cases it is the father the one who makes almost all the job, while the female is very relaxed in this respect and looking for future good fathers (see Syngnathidae and Common Suriname toad if you are interested in two examples. Also if you have time, mood, and an translator you can read this Feliz día del padre which is a sort of satyric post I wrote to reply a short sighted lamer that claimed that as a biologist she knew well that parenting was unknown in animals) . What I mean is that some sort of single fathering also exist in some species.

Coming to your question, in spite that good parents are by no means unknown among mammals, the truth is that birds practice this modality much more enthusiastically than mammals (about 6% of mammals in front of an overhelming 80% in birds. Source: Paternal care). Male mammals, certainly, have it easy to mate and go, since females have the tasks of pregnancies and breastfeeding and...well...such a long time between sex and a litter...who's gonna guess that should happen..., while female birds have -so to speak- a more fairplay start, since once they lay the eggs, they can share all the joys of reproduction with their marveled partners that have those shinning eggs to care. However, in some mammal species this trend has been reverted due, mainly, to practical considerations. Generally speaking we can find the best parents among rodents, canids and only some apes.

Rodents:

Challenge: very inmature and demanding offspring and a dangerous enviroment. Life is short and dangerous for rodents, their bet is live fast and reproduce fast. The newborns are a kind of pinky bulks unable to walk, see, and conserve heat by their own for a few days, they will have their mummy tied to them during this critical period of time. Solution?, daddy must contribute as well:

Several species of rodents have been studied as models of paternal care, including prairie voles (Microtus ochrogaster), Campbell's dwarf hamster, the Mongolian gerbil, and the African striped mouse. The California mouse (Peromyscus californicus) is a monogamous rodent that exhibits extensive and essential paternal care, and hence has been studied as a model organism for this phenomenon.

Canids:

A great source of good fathers. Their challenge is a combination of inmature puppies that need to be protected for a long period of time and the great contribution females make to hunting and defend the territory (they are working moms). Also, it helps that in many species that live in packs, only the alpha couple reproduces, so they have a lot of working hands (in reality working paws and jaws) to help.

Paternal care has never been reported as absent in any canid species, and some form of care has been seen in 18 of the 36 species in the family. Food provisioning, active defense of the young, and protecting young by remaining at the den as the female forages appear to be the commonest forms of male care. In addition males may groom, retrieve, play and rest with young. Male canids are rarely involved in den selection or construction. The effect on the fitness of the young of indirect forms of male care such as provisioning the female and territory defense are hard to assess. Quantitative studies of male provisioning in seven species offer few generalizations. In two species (Canis aureus, C mesomelas) females provided more food to the young than males; in one species (Alopex lagopus) the pair contributed equally to feeding young, and in four species (Canis lupus, Vulpes vulpes, Chrysocyon brachyurus, and Lycaon pictus), males provided more food than females. Much more data are required, particularly from field studies, before patterns of variation can be interpreted.

Certainly many mammalian males do great effort in order of growing their youngs, be it their offspring, their younger relatives or their group juveniles. Although they are not majority among mammals, because males interested only in mating and 'single mothering' -so to speak- is way far more widespread.

Source: Paternal Care in Canids

Apes:

Primates in general, and apes in particular, are not so enthusiast about devoted biparenting. In fact, wikipedia seems pparticularly laconic when mentioning paternal care in apes: "Paternal care is rare in non-human primates". (Paternal care ). I think that some concepts can be added in defense of those primates, I will do it later.

Not the most commonly known apes, gibbons, particularly siamangs, are the males that take the greatest fathering challenges, apart from humans.

A group of siamang normally consists of an adult dominant male, an adult dominant female, with offspring, infants and sometimes a subadult. The subadult usually leaves the group after attaining the age of six to eight years; subadult females tend to leave the group earlier than subadult males. Siamang gestation period is in between 6.2 and 7.9 months; after the infant is born, the mother takes care of the infant for the first year of its life.

Siamang males tend to offer more paternal care than do other members of the family Hylobatidae, taking up a major role in carrying an infant after it is about eight months old.

The infant typically returns to its mother to sleep and nurse. The infant begins to travel independently from its parents by its third year of life.

Siamang

(Excerpted from Arkive. A great site to learn about animals, and not, this is not spam).

Primates in general

Well, I will say some words in defense of how many primates practice parenting:

Although monogamy is generally rare among mammals, a number of primate species are monogamous. Extensive paternal care is a related issue but is one that is not necessarily associated with monogamy or with paternal certainty. For example, despite paternal certainty, primate mothers in monogamous species with body weights over 2 kg still remain the primary infant caretakers, while males in the communally breeding tamarins carry infants more frequently than mothers do, even in the absence of paternal certainty. Several different tactics are used by small-bodied primates to cope with the energetic burden of raising proportionately large infants in an arboreal environment: (1) infant carrying by subadult and/or related nulliparous females (Saimiri, Lemur monogoz); (2) infant carrying by fathers and offspring (Aotus, Callicebus, Saguinus, Cebuella, Leontopithecus); (3) “parking” infants while family members forage (Tarsius, Galago, Microcebus, Cheirogaleus, Varecia); or (4) some combination of the above (Callithrix, Hapalemur, Loris). Lactation length and infant growth patterns appear to influence which of these tactics is employed by a given species. Moreover, although most small-bodied, mated, monogamous female primates spend no more than 9 months annually in gestation and lactation,Aotus andCallicebus mated females are either pregnant or lactating on a year-round basis. It is this heavy female reproductive burden that may be an important factor in selection for extensive paternal care in these monogamous cebids.

Patterns of paternal care in primates

And here, in the description of these tasks carried out by other members of the group we can find a key to understand that in some species there is are some ways of sharing with the males the burdens of juvenile raising, like babysitting, or even teaching. Yes, teaching: Susana Molina's answer to Which wild animals, if any, teach their young in communities / packs / classes or other groups?