Steel is the traditional material for bike frames, which means it is tried and tested. Steel tubing has a degree of flexibility, so steel frames are compliant. This means it dampens the vibrations from the road, giving a more comfortable ride. There are types of frame construction: welded frames and lugged and brazed frames. In general, welded frames give a more responsive ride, whereas lugged and brazed frames are more compliant (flexible) and soak up more of the vibrations from the road. Almost all frames dating from the 1980s and earlier are lugged and brazed steel. Welding became commonplace in the 1990s.
Many entry-level road bikes and hybrids are made of aluminium. Aluminium frames are thought to be both lighter and stiffer than steel ones. This can make them more efficient but, in my experience, they do not dampen the road vibrations as effectively, so they can give a harsh ride. Aluminium became a popular choice in the mid 1990s, initially for mountain bikes.
Titanium is thought to give an extremely comfortable ride, due to its compliance. It also has the advantage of being very lightweight. Titanium is an expensive material and titanium frames cost many hundreds of pounds, putting them out of reach of most utility cyclists and making them a target for thieves in some urban settings. It gained popularity in the 1990s although at this stage bike manufacturers were still experimenting with construction techniques, some of which didn’t result in particularly good frames. For instance, in the mid-1990s, Raleigh bonded titanium tubes into steel lugs but some of those frames ride strangely. Titanium works best when it’s welded. Titanium doesn’t rust, so it doesn’t need to be painted.
Carbon fibre composite
Frames made from carbon fibre composite (i.e. plastic reinforced with a woven carbon fibre sheet) give an excellent combination of compliance and lightness and they are becoming cheaper year by year. However, the performance road bike manufacturers led the development of this technology and racing cyclists have different requirements than utility cyclists, and prioritise performance over practicality. There is some concern about the failure mode of carbon fibre composite components: when they break, they snap suddenly, which could be an unnecessary risk for everyday cycling. Steel has a different failure mode, bending before it breaks, so you’re more likely to notice a problem before it fails completely.
The online market has recently been flooded with inexpensive, unbranded carbon frames originating from the Far East. I would only ride a branded carbon frame from a reputable manufacturer. If a maker isn’t confident enough to put his name to it, I’m not going to ride it in traffic!