In FME, is there a way to connect multiple input feature types from reader and route to single transformer?

It's not a very well-known feature, but you need the Feature Type Connections window. You access it like this (View > Windows > Feature Type Connections):

In there select all the source feature types, select the transformer point to connect to, then click Connect:

I just came across this old question and wanted to update it with a new answer. My previous answer still stands (and is still useful in some cases), but a quicker way now (FME2016+) is to select all of the source feature types and add the transformer with Quick Add.

Then all of the feature types are automatically connected to the transformer.