I'm not sure on the first one, but on the Paph you should trim the spike down as close to the leaves as you can without damaging them.
I recently cut the spike from my first Paph and I used scisors and sloped them down following the line of the leaf, cutting as close as I could but not going inside the fold of the leaves.
Not all orchids CAN rebloom from an existing spike and Paph is one of them.
In this case the spike just dies back on it's own and you cut it for asthetic reasons. It's going to make no difference to the plant whether you cut it or not (in nature it would either stay or get nocked off by animals or something).
In other cases (such as Phals) the choice gets more difficult as they CAN rebloom from the same spike. If the spike turns brown and/or dries up (as they sometimes do) then it's just the same as on orchids which can't rebloom from the same spike.
But if the spike on something like a Phal stays green you have a choice, and from what I can tell people here on OB are split down the middle on what you should do.
If you leave the spike then that spike may grow new buds and give you more flowers quicker than you would get them if you cut the spike.
The other school of thought is that if you cut off the spike the 'chid can put it's energy in to growing for a while rather than in to flowering. This will strengthen the plant and ultimatly give you better/more flowers. Allowing the existing spike to reflower on the other hand will cause the 'chid to weaken as it puts all it's energy in to flowering.
I favour the second method, of cutting the spike and letting the plant grow and strengthen itsself.
So in summary, on your Paph there is no reason to leave the spike as it will not flower from there again, but the only reason to remove it is asthetic. With the other 'chid I'm afraid I don't know what it is and I don't know whether it is a type that can flower again. If it is one which can flower again from the same spike, then the choice of which way to go is yours.
I guess thats true.. I will probably cut the spike, cause i can wait a while before i see blooms, if it means i'll probably have more.
Thanks for that, its going to help me indefinantly with flowering orchids. I just noticed yesterday my Bulb. lasiochilum is putting up a spike, i hope. I'll take pics.