Embroidery is remarkably resiliant and can be washed in the washing machine.
However, there are a few precautions you should take beforehand, and also after you have washed it.
Firstly - if you have never washed these pieces before, then you will have to do it carefully by hand in case any of the colours run.
Always use pure soap - there is actually a brand in the US that you can get at riding shops that they use for washing horses manes (sorry - I'm in Australia and I cannot for the life of me remember what the name of this stuff is) - but it is relatively inexpensive if you buy it at a tack shop.
Don't - whatever you do - use a wool-mix type of washing liquid.
Dissolve the soap completely and then immerse your piece in the soapy water. Use cold water. Don't rub the embroidery, but swish it around the water, and then leave it to soak for about an hour.
Give it a final swish around, and then take it out, and empty the water. Rinse the piece thoroughly in cold water, until all the soap is out and the water runs clear.
Squeeze it very gently and then lay it out on folded towels.
You are going to have to re-block the piece to get it back in shape and this is the perfect time to do it.
Block out your piece (do you know how to block?) and then place anoter towel over the top of it to absorb the moisture.
When it is dry (about 24-48 hours) remove the towel, and the blocking pins.
Press ON THE WRONG SIDE lightly - on a well-padded ironing board (if you press on the wrong side, all the embroidery on the right side will stand away nicely from the fabric).
Voila - all done!
Now - if the colours did not run in future you can wash it in the washing machine using a lingerie bag on a gentle cycle.
You will, however, have to block it each time you wash it.
It is not recommended that you wash embroidery too often - especially embroidery on aida, linen or evenweave, as these fabrics are fairly loosely woven and do not stand up to it.
If your embroidery is stamped cross stitch on linen (like traced linen tablecloths, doileys, etc), then it is able to be easily washed and ironed (I have this sort of work done by my grandmother in the 1920's that has been washed and had pretty hard wear during the years and is still going strong).
I hope that this helps.