Depending on the age of your modem, and upgrades that your ISP has made since it was installed, your modem could no longer be compatable with their system. Many times an ISP will increase their speeds and the older equipment will disconect while trying to keep up. If you have ruled that out; before purchasing a new router I would recommend checking with your game console manufacturer for their compatability recommendations.
Her are the recommendations for Xbox 360
Routers
The following routers have earned the Xbox Live Compatible logo.
Microsoft Supported Firmware Wireless Standards
MN-100 1.08, 1.11.017 Wired only
MN-500 1.08, 1.11.017 802.11b
MN-700 02.00.07.0331, 02.00.08.0333, 02.01.02.0590 802.11g/b
D-Link Supported Firmware Wireless Standards
DI-524 1.05, 3.00 802.11g/b
DI-604 2.18, 3.2, 3.36, 3.51 Wired only
DI-614+ 2.18, 3.2, 3.35, 3.43 802.11b
DI-624 2.25, 2.28, 2.42, 2.50, 2.70 802.11g/b
DI-634M 2.01 802.11g/b
DI-784 2.38, 2.42 802.11a/g/b
DGL-4100 1.2, 1.3, 1.6 Wired only
DGL-4300 1.2, 1.3, 1.6 802.11g/b
WBR-1310 1.01 802.11g/b
EBR-2310 1.00 Wired Only
Linksys Supported Firmware Wireless Standards
BEFSR41 (v3) 1.04.8, 1.05.00 Wired only
BEFW11S4 (v4) 1.45.3, 1.50.14 802.11b
WRT54G (v1, v2, v3) 3.01.3, 3.03.6 802.11g/b
WRT54GS (v2) 3.37.6 802.11g/b
WRT55AG (v2) 1.10, 1.79 802.11g/b/a
Netgear Supported Firmware Wireless Standards
WGU624 1.0.1.2EN, 1.0.1.9EN 802.11g/b
WGR614 (v1) 1.40 802.11g/b
WGR614 (v5) 1.0.7_1.0.6 802.11g/b
WGR614 (v6) 1.0.11_1.0.7 802.11g/b
WGR614 (v7) v1.0.12_1.0.12NA 802.11g/b
WGT624 (v2) 4.2.6_1.0.1 802.11g/b
WGT624 (v3) 1.0.12_1.0.1, V1.0.120_1.0.1, V1.0.128_1.0.1 802.11g/b
WGT634U 1.4.1.8, 1.4.1.10 802.11g/b
WPN824 1.0.10_1.0.7, V2.0.15_1.0.11 802.11g/b
ZyXEL Supported Firmware Wireless Standards
X-550 X-550_V1.1 802.11g/b
P-330W 1.8 802.11g/b
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The WRT54G would be my choice. The S desigtnation is for Speed, however the speed boost will not improve the speed of the wireless gaming adapters (at least in the case of xbox 360)
I have used the WRT54G in our home, we have 2 wireless laptops, 1 hardwired desktop, 2 wireless xbox 360's and 1 hard wired xbox 360... All work through this router with no problems or speed loss.