Should prepaid expenses and/or deposits be classified as "current" assets or "other" assets?

I think it would depend upon the conditions of the payment. In the legal profession, for example, clients pay retainers - a pre-paid deposit toward work to be performed. The funds are supposed to be put into escrow, and as services are delivered, the attorney pays themselves from the funds. Until the services are provided, the attorney cannot treat the money as his own so it would not count as an "asset". The client can always quit the firm and any unused retainer has to be returned to them, so it remains the client's money until earned by the attorney.

In this case the funds would not really be an asset at all. It becomes an asset after it's billed and transferred from escrow into the attorney's regular accounts.

In other situations and businesses, non-refundable deposits are paid toward a product or service. I would think these deposits would immediately become an asset. In balance, the promised product or service would be a debt until it is delivered. So, for example, if you are a contractor, you might be paid 50% upfront toward a construction job for which you are to provide all the supplies and materials. So if you're building out a kitchen, you have to pay out of that for the cabinets, appliances, flooring, paint, counters, etc. It's not all "your money" - it's money toward a job. The portion for labor is yours, but there's an expectation of service so again there's a balance - the payment for labor is a credit, but the work is a debt until it has been satisfactorily performed and the laborers have been paid.

Maybe you could explain in more detail the situation you are working with.

Prepaid expenses or deposits for say, rent, are usually treated as Current Assets because their value will be extinguished in the next accounting period. Other Assets are more likely to be things like intangibles;ie; Goodwill, Patent Rights