I have been using the same pair of dynamic-driver, tower speakers ever since I bought them new in 1990. There have been at least 3 considerations I've needed to deal with over the years.
1) All the drivers have rubber surrounds, but it's still been necessary to treat them with a decent rubber preservative every few years or so, but that's very easy to do and not expensive.
2) I had the crossovers professionally refurbished in 2007. Crossovers do age, perhaps especially those with cheaper parts... I wouldn't expect you'd have to do that very often - once at some point during your ownership may well be enough. I removed the crossovers myself and shipped them to the service company, so I didn't have to deal with shipping the whole speakers. Cost: a bit less than $300 altogether.
3) Check to see if the used speakers you want use ferrofluid in the tweeters (or mids). After a few years or so (even if they've been in storage), the ferrofluid can dry out. In practice, discovering it can creep up on you and you may suddenly become aware of an otherwise unexplained channel imbalance in the highs and some loss in HF dynamics and power handling. Parts Express carries it and it's not too expensive. The only difficulty at first is learning how to remove and dismantle your tweeters so you can add some more fluid. But, then again, you would still really need to know how to do this, even if you were buying brand new speakers that use ferrofluid...just part of their maintenance. But, acquiring this skill can be a useful advantage for used speaker buyers since, often as not, they may be buying from individuals who possibly never fully understood this one real reason why they may have grown disenchanted with their performance. Anyone can take advantage of this: sellers, buyers and owners alike, but I suspect it may more commonly work for buyers and could possibly help you land a good bargain. But, in effect, I don't think there is functionally any difference between a tweeter (that's in otherwise good shape) with newly added ferrofluid and a brand new tweeter - they are essentially one and the same thing - top off their fluid and you instantly regain showroom performance from them...performance that you can easily hear.
Larryi said: "I hardly think that speaker technology is advancing such that ten year old speakers are necessarily inferior to newer models. There are MANY older designs that are terrific sounding and it is really more a matter of personal taste than technical advancement that will determine what is best". I completely agree. The old saying that there are plenty of both good and bad examples of speakers at every price point is very likely just as true today, I'm sure, as it was in 1939, so synergy together with personal preference is still the name of the game. But, many say that some of the best sounding mid and bass drivers ever produced were created from simple paper cones. If properly maintained, you can expect a good pair of speakers to last about 50 years.