Can whole chilli peppers be frozen?

Yes, they can be, but you'll want to prick each one with a sharp knife once or twice to prevent them from bursting. Once that is done, put them into a small freezer-safe storage bag, remove as much air as possible from the bag, and seal it. They keep reasonably well for about six months without tasting "burnt," but they tend to be a tad mushy upon defrosting.

I always thought the mushiness factor had to do with length of freezing time, but since you asked, I did a bit of research. Apparently, what makes chilies turn to mush actually has to do with how quickly they initially freeze:

The undesirable mushy end product that comes from freezing fruits and vegetables isn't from the act of freezing itself, but from how you freeze. Your ordinary freezer, or even deep freezer, freezes food slowly. Chilies have water in their membranes, and as they slowly freeze, it forms jagged ice crystals that pierce and puncture the membrane, so that when you defrost it, you're left with a leaky and "tenderized" result. The solution to this problem is easy … faster freezing. If the water doesn't have time to form jagged ice, you won't have a mushy membrane.

Happy Living (from which I pulled the above quotation) has an article about how to safely use dry ice to freeze chilies quickly. (I'll probably keep going the way I always have and accept the mushiness, but if you want to freeze a lot of chilies for a variety of applications, the dry-ice method looks promising.)

I freeze whole chillis without any trouble at all. They seem to work much the same afterwards, but I wouldn't want to use frozen ones for anything in which they appear substantially raw, because the texture's seriously compromised. The heat and flavour seem to be more or less unharmed though.

I grow Ghost Chilis (naga jlokia, but jolokia) and have tried freezing them, although the heat and flavour seem relatively unchanged the texture is always going to be mushy. I found drying them is a much better way to preserve them if you need to add them directly to your food, but if I am making a curry sauce or soup I use the frozen as they get chopped up and heated anyway so you don't really get the mushiness. Drying them is as simple as stringing them up in the kitchen or lay them out on a wire rack or similar, so long as air can circulate all around.

Since I don't make salsa everyday I hate to discard chilis that are given to me. I run them through a "Ninja" and then freeze them in small freezer bags. When I need to make salsa I take out a bag and with a sharp knife cut a slice off and added to my other ingredients to make a tasty salsa in the middle of winter or anytime. They never loose their flavor or heat.

I've never tried it, but the Encyclopedia of Country Living notes the following:

Freezing Food That Contains Chili Peppers : Remove the chilies before freezing, or the stuff will get hotter and hotter! To freeze chilies by themselves, chop them up first. The thick and fleshy varieties are best preserved by freezing rather than drying.

And then under the section on sweet peppers:

Freezing Sweets. Cut in half, remove seeds and pulp. Freeze your nicest ones in halves for later stuffing. Dice or slice the others. No need to blanch. Package in small plastic bags, since you make want only a little at a time. ... Never thaw peppers before using. ...

(I removed the bits about serving suggestions or specifically about pimentos, as it wasn't relevent)

You can also dry peppers by placing them on a cookie sheet and putting them in a closed car for about 3 days in the summer. It gets about 120-140 degrees in a closed car. I've dried peppers repeatedly this way. No ovens, no labor at all. Just remove stems and slice in half, place on cookie sheet, pop in car and forget it for a few days. JMP

We have a variety of whole chillies which we have frozen over 2 years ago. I read that 6 months is top to freeze them, however they still have all their colour and flavour. We cut them with scissors into tiny pieces whilst still frozen and pop them into quite a few of our dishes. The chillies we have are scotch bonnet and jalapeño, and a few different ones in all the different colours. I’m sure they will (go off) at some point but whilst still full of flavour we may as well keep them

Although not specific to that type of chilli, I freeze whole chillis I grow "as is".

They can be then cut and added to whatever dish you're preparing straight from the freezer (be it a curry, chilli con carne or even salsa)

I sometimes wonder if the chillies become slightly milder after being frozen, but I don't think the difference in heat is substantial.

If I'm not cooking with the chilli, but as a garnish, I usually put them in a soy sauce to help defrost them without making them taste mushy. (I agree that you should "never defrost the chillies", but at the same time, it's freaking weird to have cold lumps on your food!)

Freeze chillies for cooking. But if you want whole chillies to serve with a meal, store them in a glass jar with white vinegar and a tablespoon of salt. You get the taste of vinegar but the heat and flavor are as they should be. In both cases remove the stalks first.

If anything, we've found freezing whole "calcutta" chillies in freezer bags has resulted in something strange. They seem to be getting hotter as we work our way through the last bag we froze, using one chili chopped finely in a pasta sauce for two has become sufficient for a heat level between mild and medium whereas we would use two or three of the same type of chili in the past.

Of course you can also home dry all your chillies (just on a string with air circulating all round) then use same as for all dried chilli. I now have an amazing variety of dried chillies to call on. I will definitely be freezing some now, i always feel guilty going into my local indian supermarket and buying just the one or 2 i need, so constantly have extra!