How to predict the spectrum of an aliased/folded signal without looking at the FFT? This seems like a trivial concept but I just can't get the hold of it. I have a signal with two complex sinusoids having frequencies -25MHz and 17MHz. Currently it is being sampled at 64MHz so I get two peaks of fft at -25MHz and 17 MHz. If I throw every other sample away the component at 17MHz shifts to -30MHz and the one at -25MHz to 14 MHz. 

I know it is due to the aliasing/folding but why exactly are these frequency components present in the aliased signal? Is there any way to predict the frequency content of the aliased signal without looking at the fft? What spectrum should I get if every fourth sample is dropped (i.e. sampling frequency now becomes 16MHz)?
Your description of the situation is faulty.  A complex signal sampled at 64 MHz can represent frequencies from -32 MHz to +32 MHz, so the presence of tones at -25 MHz and +17MHz is fine.  However, when you decimate by two the sample rate drops to 32 MHz, and the frequency range becomes -16 MHz to +16 MHz.  In other words, you can't have a signal at -30 MHz afterwards.

The aliasing shifts the signals down to the new Nyquist zone (the region between the negative and positive Nyquist frequencies, -16 MHz and +16 MHz respectively).  -25 MHz is 9 MHz below the negative Nyquist frequency so it is shifted up by 32 MHz (the width of the Nyquist zone) to +7 MHz.  +17 MHz is 1 MHz above the positive Nyquist frequency, so it is shifted down by 32 MHz to -15 MHz.



The picture above shows the before (top plot) and after (bottom plot) frequency spectrum.  It was created with the following Matlab commands:

sig = exp(j*(1:1000)*2*pi*-25E6/64E6) + exp(j*(1:1000)*2*pi*17E6/64E6);
freq = -32E6:64E6/1000:32E6;
dec = sig(1:2:end);
freqDec = -16E6:64E6/1000:(16E6-1);
subplot(2,1,1)
plot(freq, 20*log10(abs(fftshift(fft(sig)))))
subplot(2,1,2)
plot(freqDec, 20*log10(abs(fftshift(fft(dec)))))


EDIT: I see that you largely had the right idea when you calculated the aliased frequencies.  The only mistake that you made was to not divide the frequencies by 2 due to the decimation.  Thus, -30 MHz should have been -15 MHz, and 14 MHz should have been 7 MHz.