Yes, I use them, but sparingly because some do think (me) they are couter-productive. I have read excerpts from two studies saying NSAIDs and relateds can decrease protein synthesis by as much as something like 50%. I'm not sure exactly what the percentage was, but it was high. Beyond that, "inflammation" is a natural response to trauma, which tells me it is a significant part of the healing/building process - you interrupt inflammation you interrupt the process. Basically, if pain relief is more important to me at any given moment than muscle building, I take an anti-inflammatory. If I can grin an bear it, I don't.
I have taken them during cycle but did not notice and slowing of gains. But if you are injured I would take them if neccessary in order to keep up your training.