Are landlords ever willing to negotiate the monthly rent and accept lower offers when a prospective renter submits an application?

This is purely a case-by-case situation.  There are many factors that could apply, but obviously a full offer on the asking price will generally give you best chance at securing the apartment and not losing it to another renter.  If you’re working with an agent who knows the landlord well, ask if he/she thinks you can secure the apartment at a reduced rent.  Some may allow lower offers, while others will reject your application immediately (and potentially not accept future applications, in extreme cases).

Here are some factors that could influence a landlord’s decision to agree to lower rent:

Time On Market
If an apartment is relatively new to the market (recently became available), a landlord will be less likely to accept a lower offer on it.  Conversely, if the unit has been sitting vacant for the last few weeks or longer, negotiations on price may be possible.

Seasonality
During the “off-months” (e.g. winter season, November – March) when there is less demand, landlords may be more flexible on price in order to secure a tenant and reduce vacancy.

Location
Buildings in less desirable locations (e.g. far from public transportation or across the street from a noisy bar, etc.) afford their landlords less leverage and may induce them to negotiate with prospective tenants who are willing to live there for lower rent.

Rental Building Vs. Condo / Co-op Owner
Compared with larger rental building landlords, individual condo and co-op owners may be more willing to negotiate with a prospective tenant on price, especially if the applicant has solid financials and has demonstrated a high level of credibility.  Having a solid tenant in place is extremely important for many owners, who may be willing to sacrifice some rent for a better situation.