Using the phrase "valued at market" implies the existence of a market, in which there is active, ongoing trading of the particular asset in question, and of sufficient volume that there is clearly a broad concensus of opinion as to the value of this particular asset.
For such assets, I frequently restate balance sheets to "market" values, even if this restated bal sheet is strictly an "internal-only" report, intended to provide useful information to the managers of the firm. Usually this report doesn't take the place of the "official" balance sheet, on which assets are shown at historical costs, but rather is a supplement for management's purposes only.
On the other hand people sometimes abuse the term "market value" to simply mean intrinsic economic value, current liquidation value, or something similar. In such cases it's important to remember that while such valuation numbers are important, they commonly involve a good deal of subjectivity as to cash flow estimations, discount rate assumptions, and so on. Hence, it's difficult to argue for their inclusion on the "official" published financials (at least not without some clear disclosure such as "No market exists for this asset. The amount reported here is derived from the following assumptions....").
