Yes. Drive to drive copying doesn't care whether a drive is an SSD or a spin-y disk. Definitely helps if the new disk is larger than the old (or equal size) -- you'll typically have to shrink the main partition if not, which is not an operation for the faint of heart.

In almost all cases, on a modern (e.g. not XP) version of Windows, no.

Laptops from say, 2007-2010 with XP may have their storage controller set to the wrong mode ("ATA" or "Legacy" rather than "AHCI".) This will work with SSDs, but will not be optimal for the performance or longevity of the drive.

(Laptops older than 2007, while they will work with SSDs if they have a SATA port, will not be able to even older SSDs for optimal performance -- although frankly, in a machine that old, the drive will be so much faster than that machine that the difference won't be noticeable.)

Converting it requires adding a driver, playing with some Windows settings, then shutting down, changing it in the BIOS, and then rebooting. It is a really annoying technical process, and on machines that age, I wouldn't bother to switch it unless you're reinstalling with Windows 7 or 8

What about XP ?

I just bought a couple 120GB SSDs for $59 each today and planned on using them in some older laptops that have XP on them (they came with Vista) and I do not want to pay for Windows 7 upgrade

If they already have XP, either:
(A) despite coming with Vista, the machines are too old for AHCI, or
(B) someone has already gotten the AHCI driver into XP, or
(C) someone has already disabled AHCI

(Which one might be different between the laptops.)

If you're looking at copying the image over from the old laptop to the new one, you're safe: even in case "B" the old laptop has the right driver.

If you're looking at a fresh reinstall, and you installed XP, following whatever procedure you used to do the XP install should work.

If weren't the one who installed XP, (B) is the one case that might trip you up on reinstalling it. It's pretty easy to recognize if it happens, as the XP installer will get partway in and say you have no hard drive. Fixing it requires doing an F6-driver load or slipstreaming the driver onto the CD, and if that doesn't immediately make sense to you, you probably don't want to do it.

If you have a Vista DVD and they came with Vista, unlike XP, my recollection is that Vista works with AHCI out of the box, and upgrading the machines might be worthwhile (and the memory; if they're on 2GB, Vista really does better on 4GB.)

OP, I just noticed your thread. Please see my post from another thread: http://www.flyertalk.com/forum/21878993-post51.html regarding an Acronis discount offer.

A friend who does network maintenance (involving lots of disk cloning) for a company with many hundreds of PCs strongly suggests HDClone as being easy and powerful:

http://www.miray.de/products/sat.hdclone.html

HDClone (non free version) has the ability to resize partitions on the fly which is great when your SSD is smaller than the hard drive you're cloning.