I'm struggling to believe this discussion has lasted more than 3 or 4 replies... it's quite straight forward. No landing clearance = do not land. Simple as.
If I haven't managed to get a landing clearance in on the R/T due to being too busy, I'd consider that my fault for not adequately prioritising, or not grabbing some verbose pilot and tellign them to standby, in no uncertain terms. If Mr D Umbass started giving me a life story on a busy frequency resulting in me missing a chance to give a landing clearance, I'd make Mr Umbass very aware of this fact.
In a slightly different case, consider aircraft 1 on VHF and aircraft 2 on UHF. Aircraft 1 is at 3 miles final with a clear runway ahead, however not yet with clearance. Aircraft 2 is at 6 miles and declares a mayday. Aircraft one, being VHF has no idea what is happening behind. However, if I have aircraft 2 declaring a mayday I'm going to be busy straight away, most likely alerting the crash vehicles. If I do not have time to tell aircraft 1 to go around, I expect them to do exactly that in the absence of a clearance. Should this aircraft subsequently land without clearance, the Captain is to expect major paperwork, and possibly a large jet with no brakes crashing into his ar$e.
As for 'assuring yourself that the runway is clear' - well, if that was the case there would be no need for ATC. If there is a fire on an aircraft on the other side of the runway to the fire section, I would be giving the crash crews priority over pretty much any aircraft to use the runway. If bandboxing gnd and twr, then obviously my main effort would be acknowledging and dealing with the emergency on gnd.
If you are arriving with an emergency, on the other hand, then I have no issues with the pilot doing what they consider best in order to maintain the safety of those on the aircraft and on the ground. That's why they get paid the mega-bucks.
My point is this - ATC knows what is happening on the runway/s at all times - if they do not give you clearance to use the runway, there is most likely a good reason, and you are to go around. We all make mistakes, but neglecting to give a landing clearance in the absence of a good reason is nearly unforgiveable.
I realise that I hold a very direct view on the subject, but as with a number of things in aviation, these rules are in place for the safety of all concerned. Breaking these rules as you see fit is not only unacceptable, but dangerous.
My 2c.
GBOACdave