Coincidentally I did a video today about the breadboard and prototyping methods that I use which should be up in the next couple of hours (uploading now *** Sorry, I had to re-upload, something went wrong with the transcoding ***).
https://youtu.be/5Og9MUkIeHkI use several methods, depending on the circuit. Even if the end result will be on a custom PCB, I do a lot of unit testing using the various techniques before designing and committing a complete design to a board house.
Solderless breadboards, certainly, I use them all the time, together with breakouts for SMDs. I agree with others, there are some crap ones out there. Somewhat counter-intuitively, I get mine from Maplin here in the UK, they are pretty reasonable compared to some of the cheapo crap on ebay and Amazon. I do buy the link wires from Amazon in bulk, they're not the best but they're good enough usually.
For most breakout boards for standard SMDs like SOIC/TSSOP/MSOP/QFN/QFP/SOT23 etc I go to ebay and buy in bulk and keep a reasonable stock as not a day passes without me using one or two.
For some more SMD stuff like sensitive analogue and mixed signal, I use Schmartboards which have an integrated ground plane mitigating many effects that breadboarding suffers.
Some breakouts for BGAs and slightly more exotic packages are available from Proto-Advantage, but they don't have the ground plane that Schmartboards do.
For basic soldering, I've used veroboard, particularly Tripad, for decades and continue to do so, and I mount a hybrid of both through hole and discrete SMD parts on them.
More recently after a post a few months ago here, I have started using BusBoard SMTpads surface mount boards with solid copper groundplanes and holes for optional ground vias. These are free-form like veroboard and better support things like switch mode power supplies and some analog and mixed signal stuff thanks to their solid ground planes. They're available in both 0.1" pads and 0.05" pads.
If all else fails, I make up a board and fab it myself in-house. Making the board itself is quick once you have figured out your process (figuring out the process takes a lot of failure though!), half an hour from opening the cupboard with the nasty chemicals to having a board and tidied up. For anything other than a really basic board, laying out the board typically takes quite a bit longer, as I capture the schematic at the same time (most of my designs live through their prototyping life on paper).
If I do make up the board myself, I can go down to 0.5mm pitch reliably, but I am unable to drill vias under 0.7mm without breaking drill bits, that may be my crappy drill press though, but it was advertised as being specifically for PCB drilling. Thankfully I do little through-hole on my own board layouts and usually maintain a solid ground plane on the underside so drilling is typically limited to ground vias.
Some links:
http://www.busboard.com/surfacemountpcbshttp://www.proto-advantage.com/store/index.php?cPath=4000http://schmartboard.com/surface-mount-boards/