The Eurocode proposes different limits for rare, frquent or quasi-permanent load combinations. I think they are between L/700 and L/1000 or something like that.
Greetings, as a part of the answer to your question, I would also like to add that along with the use of the deflection limit per specification you use (L/250, L/300 etc) I would also recommend to check the stress state at the particular deflection limit. If the stresses in the supporting element exceed the elastic limits, you may develop a residual plasticity problem and even a fatigue problem in the members. Fatigue in concrete is also possible.
If you are looking for deflection limits of deck slab spanning transversely over girders or stringers, there is none. However, a very flexible deck will cause deck wearing surface to perform badly, so it is best to limit the deck thickness to a certain minimum. Most US state department of transportation already specify a minimum thickness (e.g.: deck shall be minimum 8" etc.) regardless of bridge types or spans. However, for slab bridges spanning longitudinally, the same limit of L/800 for vehicular only bridges or L/1000 for combination of vehicular+pedestrian bridges still applies. Again, many US states restrict the maximum span/depth ratios of overall spans to reduce cracking and future maintenance costs (which typically decks).