Are aerosol cans allowed and safe, in checked luggage?

The US domestic answer is that aerosol toiletries are fine: the TSA says that aerosols are prohibited, "except for personal care or toiletries in limited quantities". The regulations in other countries are, I believe, broadly similar. As a random other example, Britsh Airways' dangerous goods list says (page 2) that "Non-radioactive medicinal or toilet articles (including aerosols) such as hair sprays, perfumes, colognes and medicines containing alcohol" may be carried in checked or carry-on luggage or on your person.

Why the explicit mention of radioactivity? mindcorrosive pointed out in a comment that radioactive substances are used medicinally to treat conditions including hyperthyroidism (see Wikipedia). Also, up to at least the 1960s, radioactive cosmetics were available.

It depends; it appears that some are and some are not.

If flying within the US, the FAA has a table of items that are allowed and forbidden on airplanes (either as checked or carry-on luggage). From that table, you can see that, for instance, aerosol sunscreen is allowed, pressurized whipped cream is allowed in checked luggage but not carry-on, and spray paint is completely forbidden.

If in any doubt, you should check with the airline agent (when checking luggage), or the security officers at the checkpoint (for carry-on).

Whether or not allowed and whether or not safe is essentially the one issue. That is, if 'safe' they are allowed and if 'unsafe' they are disallowed.

Safety here (as usual!) is somewhat subjective† (eg say a controlled drug) but for aerosol cans is more a matter off flammability than pressure. As mentioned by @Mark Mayo most large passenger plane cargo holds are pressurized, even if not to pressure at ground level. For an example of subjective, most airlines deem liquid volumes over 100ml 'unsafe' even though exactly the same liquid in a smaller quantity is deemed 'safe'.

For flammability, there are two aspects: 1) the content and 2) the propellant.

As mentioned by @Nat Eldredge, some content is allowed and some not. For US domestic flights a place to check is TSA's site as he suggested. There may be some items that are disallowed despite not being flammable (and therefore in reality 'safe') on the 'subjective' basis that the majority of such items are flammable (eg perhaps water-based spray paint) - it is simply not practical to cover every single possible item that someone might want to transport, so a 'broad brush' approach has to be taken.

Propellants are usually flammable but when used for toiletries are normally in small quantity, hence allowed as for small quantities of most liquids.

† TSA governs USA, EASA the EU and IATA 'fills in the gaps'. The wording at least of each differs, hence the scope for interpretation differs, hence back to an element of 'subjectivity'.