Examples I'm familiar with:
Intel 865Gx boards. If AGP graphics are used (a GPU adapter card plugged into the AGP slot) then it works on the discrete AGP 8x bus exactly as expected. But, if Intel Extreme integrated graphics are used, then the chipset logically implements a "virtual" AGP device which directs the internal IHA bus to connect the GMCH video memory to the ICH5 (PCI hub) to allow software to "see" a display device, end result = an "AGP 8x" display which occupies (and is limited to) the bandwidth on the PCI bus.
The same workaround is done on many older Intel boards (810, 815/815E/815EG/815G, 845Gx; I don't know about 820x boards because I entirely avoided RDRAM), all using Intel AHA, virtual AGP devices identified as AGP 1x/2x/4x (and still limited by PCI bus bandwidth, regardless of label).
Others chipsets I know suck this way (but never owned): VIA (Apollo PME133, Apollo ProSavage PM133, Apollo Savage PL133T, ProSavage8 P4M266, PM800x; using VIA V-Link architecture equivalent to Intel AHA), ALi/ULi (Aladdin Pro 4 TNT2; no advanced architecture = default slow mobo bus), SiS (620, 630x, 650, 651, 661GX, 730S; sometimes using SiS MuTIOL architecture, faster than AHA when implemented but mobo default otherwise, many inefficiencies severely bottleneck practical mobo bus).
Worth noting are all VIA K-chipsets (for AMD), ATI Radeon IGP chipsets (330, 340, PRO 9000/9100, Xpress 200 RS400/410, 320; using ATI A-Link architecture equivalent to Intel AHA), and nVidia IGP/SPP chipsets (nForce 420, nForce2 IGP; using nVidia HyperTransport architecture, much faster than Intel AHA). These all implement discrete AGP logic and entirely avoid crossbussing; unsurprising, since they were all designed for maximum graphics performance.
There are many Celeron-mobile, Xeon, Sempron, and Opteron chipsets that I'm not familiar with. Truth be known, I tend to focus on Intel chipsets (on Intel CPUs), I select VIA chipsets carefully (on AMD CPUs, usually with ATI GPUs) because their products cover the entire quality spectrum from very-top to mid-bottom (and are typically inferior to their Intel counterparts for Intel processors), and I absolutely never buy the half-obsolete cheap bull**** ALi/ULi and SiS make (under a variety of misleading/temporary brands, so they don't tarnish their "real" brand names as much). Astonishingly, after being purchased by Gateway, SiS has attempted to emerge as a leader and their 740 and 741x chipsets were actually better than the Intel and VIA counterparts of the time they competed against (they correct MuTIOL flaws and avoid crossbussing, although they address less maximum physical memory).
PCIe-AGP hybrid boards (those using Intel 9xx or later chipsets, though I think AGP was fully abandoned before the PQ960-series) use a similar approach to logically link AGP into the PCIe bus, consuming PCIe bandwidth. It's possible that some continued to link AGP to the PCI bus instead but I've never seen one ("AGP" bandwidth would continue to be bottlenecked by PCI bus bandwidth; I've never actually had a PCIe-AGP hybrid board, just went straight to pure PCIe).
More modern chipsets (basically anything post Intel LGA775 or AMD AM2) don't suffer from these bus crossing issues because all the bus logic (with the exception of after-chipset PCIe lanes or USB hubs) are handled discretely by the chipset. AGP is nearly extinct. PCI is now considered a "legacy" bus.
Of course if your mobo isn't made by a top-tier manufacturer then all bets are off because they don't always implement all the hardware the chipset is designed to support. Alternatively, "super" mobos often pack extra onboard logic which exceeds the base chipset specifications (rarely in ways that increase maximum performance; but in ways that reduce/eliminate existing hardware performance bottlenecks or simply allow more hardware to be supported; ASUS P7P55 WS Supercomputer mobo is one recent example). Not all implementations are equal, especially at the highest and lowest ends of the mobo market.
