Okay, start off with the
Grundig M300PE- $30
For the price, if you aren't after a crank generator, this is it for "regular" emergency or EDC use. I've used one of these and it probably has the best built in antenna and is top5 on sound. And it does a LOT.
If it had a 24 hour clock and a hard wired antenna connector it would be perfect for it's bands and capabilities.
Grundig YB-300PE - $50
What it does that the above one doesn't- more bands, direct freq entry, scanning, memories, 24 hour clock, long wire antenna plug in. Comes with an external roll up antenna. If you don't mind going 13 ounces, it's got a lot of features that matter.
Sangean PT-633 $55
Good 9 band SW with standard AM and FM, analog tuning, dual timezone 24 hour clock.
Excellent receiver stages, limited mostly by not having the antenna connectors. (antennas are IMPORTANT).
Sangean ATS404
I love this one. It's $80, though, and if I was spending more than $50 I'd want SSB support....
14SW bands, 45 memories, manual or direct entry tuning, 24 hour clock and all the regular alarm functions all the above radios have.
ALL THE ABOVE RADIOS have a serious limit- along with most of the radios previously posted. They only get broadcast bands (and limited AM ham bands). Okay, if broadcast is all you want or need, and there's hours of fun listening on the shortwave bands. And real information from around the world. You NEED antennas to do well with this, but it's amazingly simple stuff to do. The m300PE is the winner for this segment due to cost and reception.
The above isn't exhaustive in survey, but adds to what has been mentioned.
If there's a serious crash, or emergencies where you may find yourself needing to listen to full rescue operations, or the only news getting out of a place is on SSB ham bands- you need a bit more capability. *IF* you have a license, you want one of these anyway, because then you can carry a small portable cheap low power transmitter for cw or ssb and you've got your receiver stage already.
If you don't have your license, get it

It's that easy. Then get the kenwood th-f6a and all your listening needs are covered. (the Yaesu doesn't get ssb, and that's important)
Next batch:
Sangean PT-80 $160
best buy for a consumer style SSB capable AM/FM/SW/LW receiver with good antenna support. Dual time clock, 24 hour clock, alarms, 45 memories, auto tune works well, external antenna jack (antenna included for that) for sw/lw.
This thing rocks. hard core. seriously.
The sangean ATS-909 is the end all be all for consumer style portables, though. extra tuning functions (like wide/narrow bandwidth switch to recuce interference) and programming make it a lot of radio. has manual entry AND a tuning knob. Of course, does SSB. Really sweet, gearnut radio. 2 pounds. $250.
Kaito KA1102- $80, best value for SSB
Includes rechargable batteries, ac adaptor (charges batteries), clock, 3 alarms, sensitivity settings, antenna jack for external antenna.
It does MOST everything the ATS-909 does, on a budget. I could take this out into the woods and do 95% of what I do from my radio shack at home in terms of listening, broadcast or ham. Accepts the standard roll up antenna with mini plug (3.5mm jack).
If you want a consumer style radio and you are going for more than the grundig M300PE, get this. it's small, too- about 4x6x1
But the end all be all is still the Icom R20- $500 and worth every penny. It's a handheld, 10 ounces, accepts regular options like removable battery packs, car charges, computer programming software. BNC antenna connector, you can hook this up to a CIA antenna farm with an antenna switch and hear everything. EVERYTHING. Actually, you have to buy the government model to hear EVERYTHING, the civilian model has a few bands blocked for legal reasons- like cellular. Oh, it does programmable priority alerts so you won't miss things
There's a yaesu vr-500 that does most of the same stuff for $300, but if I am going to spend Serious Money, I'll get the Icom. The yaesu will do more than well enough, though. It's a fantastic radio, and if I just couldn't go $500, but wanted more than the consumer style kaito, I'd get this. No regrets at all. (and i already have the programming software and cable)
notes: AM is the most common for broadcast on sw, but SSB is the most common voice mode for ham operators on SW and LW. There's a few AM beacons or emergency transmitters on LW, but most of what you will hear is SSB. This can be important, as much of the SAR or emergency services comms for extended areas of operation or large disasters will include a ham radio volunteer communications network.
Bands- the more you can receive, the more you'll hear. 90% of your short range ham emergency traffic will be in the 2m band on FM type comms, for example. And some of the lower band- 40 and 80 meter - stuff is going to be more important than getting broadcast FM in some types of emergencies (especially if you are listening to stuff happening outside your immediate area)
Antennas- these are what gather the waves. the more you can gather, the better. It's that simple. Built in whips are good to have, but it's the roll ups and the homemade long wires that are going to really get you going. the pocket rollup is a good start, but it's not hard to do better homebrewing something that will ride in the radio case along with the radio. it's just wire and connectors.