Modern bottom brackets use a sealed bearing type construction that keeps water and debris locked out, so they seldom go wrong. Maintenance is impossible so they need replacing when they do wear out. Older style cup bottom brackets need to be re-greased every now and again, and occasionally will need to have their bearings replaced. There are a lot more teeth on the chainring cogs than those on the rear cassette, so need changing less regularly. Cranks usually a solid one piece construction so there is not much to go wrong.
Brakes come in a variety of designs depending on the age and style of your bike. Rim brakes offer more modulation but have less stopping power, so are more suited to riding on the roads. Disc brakes can provide huge amounts of stopping power so are best suited to off road riding, although ‘V’ rim brakes are also well suited to mountain biking. All brakes use a friction system to stop the movement of the wheel, so regular checks of the contact pads should form part of your regular cycle maintenance.