depends on how old the glue is. strip off as much of the base tape as possible by hand, then test remove some of the glue. if it is dry and hard and crunchy when you scrape or pick it off, it's toast and the glue can, in fact, MUST, be removed as much as possible. a brass wire wheel or brush works wonders for this. any shreds of old tape will come off at this time. using a steel wire brush is a bit faster but is likely to damage any anodising on the rim.

if the glue still has some stickiness or rubbery feel to it, it can probably be left on and used as the base coat of a new glue job. you will have to carefully pick out any tape remains you can find. fill any bare areas with more glue than you use on the rest of the built up areas to minimise lumpy bits under the new tire. the solvent in the new glue will dissolve the old glue and bond it together.

the rubber in the glue eventually oxidises to a point where it is so cross-linked it cannot flow at all, and that's when it's dry and dead. but for the first few years it is on the rim, you should be able to revive it with new glue.

do not run the old tire with the old base tape. that's asking for serious separation trouble, and you only discover that at maximum lean going downhill, which tends to be painful... if the glue is old enough to be dry and crunchy, you're probably best off using completely new tires.

edit: you talking about the rims or the tires?