In the Netherlands it really depends on the local situation what happens.
A specific case which came to mind when seeing this topic was Breukelen: as of December 14th, 2008 the Sprinter service between Breukelen and Utrecht had it's frequency increased to every 15 minutes. At the same date bus 130, which used to run via the highway from Vinkeveen to Utrecht, was terminated in Breukelen. And bus 120 serving the villages along the railway between Amsterdam and Breukelen had it's route changed: a loop from the village Breukelen across the Amsterdam-Rhine Canal to Breukelen station was added and the route was terminated short in Maarssen.
The last change however resulted in such a lot of complaints that already as of December 14th, 2008 a temporary route 20 bus from Maarssen to Utrecht was introduced and as of March 2009 bus 120 ran till Utrecht Central Station again. The loop via Breukelen station however still exists today.
And though the connections are certainly used (the 130 bus even has an awkward 10/20 interval to improve transfer times to the trains), there still are people using the bus all the way to Utrecht mainly for fare reasons.
Another example is the Alblasserwaard where until 2006 buses ran parallel to the railway between Sliedrecht and Gorinchem. As of 2007 both the trains and the buses were tendered as one franchise which was won by Arriva. Though service improvements would take a few years as additional tracks needed to be built, the buses and trains were immediately transformed into an integrated network with regards to fares and services.
The bus from Rotterdam to Gorinchem was shortened to Sliedrecht and parallel to the railway a separate bus service was introduced with smaller buses and more designed to connect the villages along the railway with the stations. Initially that bus ran from Sliedrecht to Gorinchem, but when Boven-Hardinxveld station was opened the bus route was changed to terminate there as the route from Boven-Hardinxveld to Gorinchem was just a long dike through nothing. And nowadays this area is served by a neighboorhood bus serving the villages of Boven-Hardinxveld, Hardinxveld, Giessendam and Giessenburg and connecting them to the three stations the municipality of Hardinxveld-Giessendam now has.